Toeplitz operators on finite and infinite dimensional spaces with associated psi *-Fréchet algebras

The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.

The factorization method for real elliptic problems

The Factorization Method localizes inclusions inside a body from measurements on its surface. Without a priori knowing the physical parameters inside the inclusions, the points belonging to them can be characterized using the range of an auxiliary operator. The method relies on a range characterization that relates the range of the auxiliary operator to the measurements and is only known for very particular applications. In this work we develop a general framework for the method by considering symmetric and coercive operators between abstract Hilbert spaces. We show that the important range characterization holds if the difference between the inclusions and the background medium satisfies a coerciveness condition which can immediately be translated into a condition on the coefficients of a given real elliptic problem. We demonstrate how several known applications of the Factorization Method are covered by our general results and deduce the range characterization for a new example in linear elasticity.

Pseudodifferentialoperatoren mit nichtregulären banachraumwertigen Symbolen

Untersucht werden in der vorliegenden Arbeit Versionen des Satzes von Michlin f¨r Pseudodiffe- u rentialoperatoren mit nicht-regul¨ren banachraumwertigen Symbolen und deren Anwendungen a auf die Erzeugung analytischer Halbgruppen von solchen Operatoren auf vektorwertigen Sobo- levr¨umen Wp (Rn

On moduli spaces of semistable sheaves on K3 surfaces

Ich untersuche die nicht bereits durch die Arbeit "Singular symplectic moduli spaces" von Kaledin, Lehn und Sorger (Invent. Math. 164 (2006), no. 3) abgedeckten Fälle von Modulräumen halbstabiler Garben auf projektiven K3-Flächen - die Fälle mit Mukai-Vektor (0,c,0) sowie die Modulräume zu nichtgenerischen amplen Divisoren - hinsichtlich der möglichen Konstruktion neuer Beispiele von kompakten irreduziblen symplektischen Mannigfaltigkeiten. Ich stelle einen Zusammenhang zu den bereits untersuchten Modulräumen und Verallgemeinerungen derselben her und erweitere bekannte Ergebnisse auf alle offenen Fälle von Garben vom Rang 0 und viele Fälle von Garben von positivem Rang. Insbesondere kann in diesen Fällen die Existenz neuer Beispiele von kompakten irreduziblen symplektischen Mannigfaltigkeiten, die birational über Komponenten des Modulraums liegen, ausgeschlossen werden.

Aleatory Sovereignty and the Rule of Sensitive Spaces

Addressing life in borders and refugee camps requires understanding the way these spaces are ruled, the kinds of problems rule poses for the people who live there, and the abilities of inhabitants to remake their own lives. Recent literature on such spaces has been influenced by Agamben's notion of sovereignty, which reduces these spaces and their residents to abstractions. We propose an alternate framework focused on what we call aleatory sovereignty, or rule by chance. This allows us to see camps and borders not only as the outcomes of humanitarian projects but also of anxieties about governance and rule; to see their inhabitants not only as abject recipients of aid, but also as individuals who make decisions and choices in complex conditions; and to show that while the outcome of projects within such spaces is often unpredictable, the assumptions that undergird such projects create regular cycles of implementation and failure.

Social Policy Facing the Problems of Youth Employment

Rumiana Stoilova (Bulgaria). Social Policy Facing the Problems of Youth Employment. Ms. Stoilova is a researcher in the Institute of Sociology in Sofia and worked on this project from October 1996 to September 1998. This project involved collecting both statistical and empirical data on the state of youth employment in Bulgaria, which was then compared with similar data from other European countries. One significant aspect was the parallel investigation of employment and unemployment, which took as a premise the continuity of professional experience where unemployment is just a temporary condition caused by external and internal factors. These need to be studied and changed on a systematic basis so as to create a more favourable market situation and to improve individuals' resources for improving their market opportunities. A second important aspect of the project was an analysis of the various entities active on the labour market, including government and private institutions, associations of unemployed persons, of employers or of trade unions, all with their specific legal powers and interests, and of the problems in communication between these. The major trends in youth unemployment during the period studied include a high proportion of the registered unemployed who are not eligible for social assistance, a lengthening of the average period of unemployment, an increase in the percentage of people who are unemployed for the first time and an increasing percentage of these who are not eligible for assistance, particularly among newly registered young people. At the same time the percentage of those for who work has been found is rising and during the last three years an increasing number of the unemployed have started some independent economic activity. Regional differences are also considerable and in the case of the Haskovo region represent a danger of losing the youngest generation, with resulting negative demographic effects. One major weakness of the existing institutional structure is the large scale of the black labour market, with clear negative implications for the young people drawn into it. The role of non-governmental organisations in providing support and information for the unemployed is growing and the government has recently introduced special preferences for organisations offering jobs to unemployed persons. Social policy in the labour market has however been largely restricted to passive measures, mostly because of the risk that poverty poses to people continuously excluded from the labour market. Among the active measures taken, well over half are concerned with providing jobs for the unemployed and there are very limited programmes for providing or improving qualifications. The nature of youth employment in Bulgaria can be seen in the influence of sustained structures (generation) and institutions (family and school). Ms. Stoilova studied the situation of the modern generation through a series of profiles, mostly those of continuously unemployed and self-employed persons, but also distinguishing between students and the unemployed, and between high school and university students. The different categories of young people were studied in separate mini-studies and the survey was carried out in five town in order to gather objective and subjective information on the state of the labour market in the different regions. She conducted interviews with several hundred young people covering questions of family background, career plans, attitudes to the labour situation and government measures to deal with it, and such questions as independence, mobility, attitude to work, etc. The interviews with young people unemployed for a long period of time show the risk involved in starting work and its link with dynamics of economic development. Their approval of structural reforms, of the financial restrictions connected with the introduction of a currency board and the inevitability of unemployment was largely declarative. The findings indicate that the continuously unemployed need practical knowledge and skills to "translate" the macroeconomic realities in concrete alternatives of individual work and initiative. The unemployed experience their exclusion from the labour market not only as a professional problem but also as an existential threat, of poverty, forced mobility and dependence on their parents' generation. The exclusion from the market of goods and services means more than just exercising restraint in their consumption, as it places restrictions on their personal development. Ms. Stoilova suggests that more efficient ways of providing financial aid and mobilisation are needed to counteract the social disintegration and marginalisation of the continuously unemployed. In measuring the speed of reform, university students took both employment opportunities and the implementation of the meritocratic principle in employment into account. When offered a hypothetical choice between a well-paid job and work in one's own profession, 62% would prefer opt for the well-paid job and for working for a company that offered career opportunities rather than employment in a family or own company. While most see the information gained during their studies as useful and interesting, relatively few see their education as competitive on a wider level and many were pessimistic about employment opportunities based on their qualifications. Very similar attitudes were found among high school students, with differences being due rather to family and personal situations. The unemployed, on the other hand, placed greater emphasis on possibilities of gaining or improving qualifications on a job and for the opportunities it would offer for personal contacts. High school students tend to attribute more significance to opportunities for personal accomplishment. A significant difference that five times fewer high school students were willing to work for state-owned companies, and many fewer expected to find permanent employment or to find a job in the area where they lived, Within the family situation, actual support for children seems to be higher than the feelings of confidence expressed in interviews. The attitudes of the families towards past experience seems to be linked with their ability to cope with the difficulties of the present, with those families which show an optimistic and active attitude towards the future having a greater respect for parents experience and tolerance in communication between parents and children.

Functional regulatory spaces

This article develops the concept of “Functional Regulatory Space” (FRS) in order to analyze the new forms of State action addressing (super) wicked problems. A FRS simultaneously spans several policy sectors, institutional territories and levels of government. It suggests integrating previous policy theories that focused on “boundary-spanning regime,” “territorial institutionalism” or multi-level governance. The FRS concept is envisaged as a Weberian “ideal-type” of State action and is applied to the empirical study of two European cases of potential FRS: the integrated management of water basins and the regulation of the European sky through functional airspace blocks. It will be concluded that the current airspace regulation does match the ideal-type of FRS any better than the water resource regulation does. The next research step consists in analyzing the genesis and institutionalization of potential FRS addressing other (super) wicked problems such as climate change and economic, security, health and immigration issues in different institutional contexts as well as at various levels of governance.

Transformaciones territoriales y análisis geográfico en ámbitos patagónicos de montaña : La comarca andina del paralelo 42

El estudio de las transformaciones territoriales en esta parte del Sur del país obedece en especial a dos circunstancias de distinta índole. La primera vinculada a la investigación y su potencial trascendencia teórica y práctica en contextos académicos y profesionales interesados por comprender las características de la instalación humana en ámbitos sujetos a importantes cambios. La segunda responde al desenvolvimiento incierto de las comarcas andino patagónicas frente a hechos, propuestas y proyectos referentes a cuestiones de decisiva impronta regional. Se trata de territorios en plena gestación identitaria, donde es habitual lo dubitativo y confuso, aún desde perspectivas históricas y literarias, que son en las que normalmente se asientan las raíces regionales. En los recientes años '90 y en concordancia con los ajustes propios del nuevo orden mundial, se observan re-acomodamientos locales inscriptos en modalidades que obligan a la revisión profunda. Modalidades postmodernas que pueden identificarse como espacios de consumo. Es la condición cultural la que imprime nuevas estructuras espaciales de fuertes proyecciones anímicas enraizadas en lo simbólico y lo estético, donde las transformaciones se suceden a partir de una resignificación de la naturaleza. Desde allí es que se hacen planteos hipotéticos en busca de explicaciones, atendiendo a las valorizaciones que existen para con la Patagonia Andina. Aquellas que implican una preeminencia singular de los aspectos afectivos y emocionales por sobre los económicos, aunque con el turismo como el vector principal de transformación y a cuyo derredor se entremezclan situaciones conflictivas. Es ésta la dirección del análisis que busca esclarecer dudas a partir de la producción de conocimiento geográfico con sentido 'examinador' de la realidad. Fenómenos como los de dispersión, neoruralidad y fragmentación espacial, se muestran como los resultados más visibles en materia paisajística y con ello estamos ante un marco problemático y complejo. Con la sistematización de una significativa cantidad de información involucrada y una fuerte carga empírica proveniente de la convivencia profesional de varios años con la mayor parte de los problemas abordados, se presenta un aporte al cuerpo teórico de la Geografía preocupada por los ámbitos montanos, así como también su proyección hacia la explicación geográfica regional y su eventual insumo para el Planeamiento y la Gestión Territorial. Se analiza el conjunto territorial ofreciendo una perspectiva integradora en escenarios novedosos que, desde nuestra disciplina pueden abordarse con la posibilidad cierta de orientar una importante cantidad de estudios sectoriales que ya se manifiestan, en particular por requerimientos políticos. Con la Comarca Andina del Paralelo 42 en el foco del análisis, la tesis se abocó a incursionar en la realidad andino patagónica, identificando, sistematizando y valorando los conflictos de estirpe territorial como camino explicativo.

A paradox : Increased psicho-social problems-less counselling intervention

This work is based upon conclusions drawn from the research project: "A Profile of vocational occupational counselling and placement and employment services" in La Plata and greater La Plata (Province of Buenos Aires, Argentina). This research was carried out between 1998 and 2002 and explored four axes or systems: Health - Labour-Social Policies and Education. In the case of this last axis, reference was made to information about school counselling teams (psychologists, psycho-pedagogues, social workers, etc.) who should have the responsibility for the counselling task, and moved their activity towards the attention of urgencies requested by educational institutions, to cope with current psycho-social problems, losing sight of the importance of counselling from a prevention perspective, for avoiding possible risk situations. Results achieved within this context (La Plata, capital of the Province of Buenos Aires, Ensenada and Berisso), due to the strategic importance of the region in the national context, allowed us to establish meaningful relationships, correlations and projective inferences in other social and regional spheres.

Transformaciones territoriales y análisis geográfico en ámbitos patagónicos de montaña : La comarca andina del paralelo 42

El estudio de las transformaciones territoriales en esta parte del Sur del país obedece en especial a dos circunstancias de distinta índole. La primera vinculada a la investigación y su potencial trascendencia teórica y práctica en contextos académicos y profesionales interesados por comprender las características de la instalación humana en ámbitos sujetos a importantes cambios. La segunda responde al desenvolvimiento incierto de las comarcas andino patagónicas frente a hechos, propuestas y proyectos referentes a cuestiones de decisiva impronta regional. Se trata de territorios en plena gestación identitaria, donde es habitual lo dubitativo y confuso, aún desde perspectivas históricas y literarias, que son en las que normalmente se asientan las raíces regionales. En los recientes años '90 y en concordancia con los ajustes propios del nuevo orden mundial, se observan re-acomodamientos locales inscriptos en modalidades que obligan a la revisión profunda. Modalidades postmodernas que pueden identificarse como espacios de consumo. Es la condición cultural la que imprime nuevas estructuras espaciales de fuertes proyecciones anímicas enraizadas en lo simbólico y lo estético, donde las transformaciones se suceden a partir de una resignificación de la naturaleza. Desde allí es que se hacen planteos hipotéticos en busca de explicaciones, atendiendo a las valorizaciones que existen para con la Patagonia Andina. Aquellas que implican una preeminencia singular de los aspectos afectivos y emocionales por sobre los económicos, aunque con el turismo como el vector principal de transformación y a cuyo derredor se entremezclan situaciones conflictivas. Es ésta la dirección del análisis que busca esclarecer dudas a partir de la producción de conocimiento geográfico con sentido 'examinador' de la realidad. Fenómenos como los de dispersión, neoruralidad y fragmentación espacial, se muestran como los resultados más visibles en materia paisajística y con ello estamos ante un marco problemático y complejo. Con la sistematización de una significativa cantidad de información involucrada y una fuerte carga empírica proveniente de la convivencia profesional de varios años con la mayor parte de los problemas abordados, se presenta un aporte al cuerpo teórico de la Geografía preocupada por los ámbitos montanos, así como también su proyección hacia la explicación geográfica regional y su eventual insumo para el Planeamiento y la Gestión Territorial. Se analiza el conjunto territorial ofreciendo una perspectiva integradora en escenarios novedosos que, desde nuestra disciplina pueden abordarse con la posibilidad cierta de orientar una importante cantidad de estudios sectoriales que ya se manifiestan, en particular por requerimientos políticos. Con la Comarca Andina del Paralelo 42 en el foco del análisis, la tesis se abocó a incursionar en la realidad andino patagónica, identificando, sistematizando y valorando los conflictos de estirpe territorial como camino explicativo.

A paradox : Increased psicho-social problems-less counselling intervention

This work is based upon conclusions drawn from the research project: "A Profile of vocational occupational counselling and placement and employment services" in La Plata and greater La Plata (Province of Buenos Aires, Argentina). This research was carried out between 1998 and 2002 and explored four axes or systems: Health - Labour-Social Policies and Education. In the case of this last axis, reference was made to information about school counselling teams (psychologists, psycho-pedagogues, social workers, etc.) who should have the responsibility for the counselling task, and moved their activity towards the attention of urgencies requested by educational institutions, to cope with current psycho-social problems, losing sight of the importance of counselling from a prevention perspective, for avoiding possible risk situations. Results achieved within this context (La Plata, capital of the Province of Buenos Aires, Ensenada and Berisso), due to the strategic importance of the region in the national context, allowed us to establish meaningful relationships, correlations and projective inferences in other social and regional spheres.

A paradox : Increased psicho-social problems-less counselling intervention

This work is based upon conclusions drawn from the research project: "A Profile of vocational occupational counselling and placement and employment services" in La Plata and greater La Plata (Province of Buenos Aires, Argentina). This research was carried out between 1998 and 2002 and explored four axes or systems: Health - Labour-Social Policies and Education. In the case of this last axis, reference was made to information about school counselling teams (psychologists, psycho-pedagogues, social workers, etc.) who should have the responsibility for the counselling task, and moved their activity towards the attention of urgencies requested by educational institutions, to cope with current psycho-social problems, losing sight of the importance of counselling from a prevention perspective, for avoiding possible risk situations. Results achieved within this context (La Plata, capital of the Province of Buenos Aires, Ensenada and Berisso), due to the strategic importance of the region in the national context, allowed us to establish meaningful relationships, correlations and projective inferences in other social and regional spheres.

Transformaciones territoriales y análisis geográfico en ámbitos patagónicos de montaña : La comarca andina del paralelo 42

El estudio de las transformaciones territoriales en esta parte del Sur del país obedece en especial a dos circunstancias de distinta índole. La primera vinculada a la investigación y su potencial trascendencia teórica y práctica en contextos académicos y profesionales interesados por comprender las características de la instalación humana en ámbitos sujetos a importantes cambios. La segunda responde al desenvolvimiento incierto de las comarcas andino patagónicas frente a hechos, propuestas y proyectos referentes a cuestiones de decisiva impronta regional. Se trata de territorios en plena gestación identitaria, donde es habitual lo dubitativo y confuso, aún desde perspectivas históricas y literarias, que son en las que normalmente se asientan las raíces regionales. En los recientes años '90 y en concordancia con los ajustes propios del nuevo orden mundial, se observan re-acomodamientos locales inscriptos en modalidades que obligan a la revisión profunda. Modalidades postmodernas que pueden identificarse como espacios de consumo. Es la condición cultural la que imprime nuevas estructuras espaciales de fuertes proyecciones anímicas enraizadas en lo simbólico y lo estético, donde las transformaciones se suceden a partir de una resignificación de la naturaleza. Desde allí es que se hacen planteos hipotéticos en busca de explicaciones, atendiendo a las valorizaciones que existen para con la Patagonia Andina. Aquellas que implican una preeminencia singular de los aspectos afectivos y emocionales por sobre los económicos, aunque con el turismo como el vector principal de transformación y a cuyo derredor se entremezclan situaciones conflictivas. Es ésta la dirección del análisis que busca esclarecer dudas a partir de la producción de conocimiento geográfico con sentido 'examinador' de la realidad. Fenómenos como los de dispersión, neoruralidad y fragmentación espacial, se muestran como los resultados más visibles en materia paisajística y con ello estamos ante un marco problemático y complejo. Con la sistematización de una significativa cantidad de información involucrada y una fuerte carga empírica proveniente de la convivencia profesional de varios años con la mayor parte de los problemas abordados, se presenta un aporte al cuerpo teórico de la Geografía preocupada por los ámbitos montanos, así como también su proyección hacia la explicación geográfica regional y su eventual insumo para el Planeamiento y la Gestión Territorial. Se analiza el conjunto territorial ofreciendo una perspectiva integradora en escenarios novedosos que, desde nuestra disciplina pueden abordarse con la posibilidad cierta de orientar una importante cantidad de estudios sectoriales que ya se manifiestan, en particular por requerimientos políticos. Con la Comarca Andina del Paralelo 42 en el foco del análisis, la tesis se abocó a incursionar en la realidad andino patagónica, identificando, sistematizando y valorando los conflictos de estirpe territorial como camino explicativo.

A set of canonical problems in sloshing. Part 0: Experimental setup and data processing

In a series of attempts to research and document relevant sloshing type phenomena, a series of experiments have been conducted. The aim of this paper is to describe the setup and data processing of such experiments. A sloshing tank is subjected to angular motion. As a result pressure registers are obtained at several locations, together with the motion data, torque and a collection of image and video information. The experimental rig and the data acquisition systems are described. Useful information for experimental sloshing research practitioners is provided. This information is related to the liquids used in the experiments, the dying techniques, tank building processes, synchronization of acquisition systems, etc. A new procedure for reconstructing experimental data, that takes into account experimental uncertainties, is presented. This procedure is based on a least squares spline approximation of the data. Based on a deterministic approach to the first sloshing wave impact event in a sloshing experiment, an uncertainty analysis procedure of the associated first pressure peak value is described.

A computer vision approach for weeds identification through Support Vector Machines

This paper outlines an automatic computervision system for the identification of avena sterilis which is a special weed seed growing in cereal crops. The final goal is to reduce the quantity of herbicide to be sprayed as an important and necessary step for precision agriculture. So, only areas where the presence of weeds is important should be sprayed. The main problems for the identification of this kind of weed are its similar spectral signature with respect the crops and also its irregular distribution in the field. It has been designed a new strategy involving two processes: image segmentation and decision making. The image segmentation combines basic suitable image processing techniques in order to extract cells from the image as the low level units. Each cell is described by two area-based attributes measuring the relations among the crops and weeds. The decision making is based on the SupportVectorMachines and determines if a cell must be sprayed. The main findings of this paper are reflected in the combination of the segmentation and the SupportVectorMachines decision processes. Another important contribution of this approach is the minimum requirements of the system in terms of memory and computation power if compared with other previous works. The performance of the method is illustrated by comparative analysis against some existing strategies.