Orbits of operators commuting with the Volterra operator

Asymptotic estimates of the norms of orbits of certain operators that commute with the classical Volterra operator V acting on L-P[0,1], with 1 0, but also to operators of the form phi (V), where phi is a holomorphic function at zero. The method to obtain the estimates is based on the fact that the Riemann-Liouville operator as well as the Volterra operator can be related to the Levin-Pfluger theory of holomorphic functions of completely regular growth. Different methods, such as the Denjoy-Carleman theorem, are needed to analyze the behavior of the orbits of I - cV, where c > 0. The results are applied to the study of cyclic properties of phi (V), where phi is a holomorphic function at 0.

New results on a classical operator

It is remarkable how the classical Volterra integral operator, which was one of the first operators which attracted mathematicians' attention, is still worth of being studied. In this essentially survey work, by collecting some of the very recent results related to the Volterra operator, we show that there are new (and not so new) concepts that are becoming known only at the present days. Discovering whether the Volterra operator satisfies or not a given operator property leads to new methods and ideas that are useful in the setting of Concrete Operator Theory as well as the one of General Operator Theory. In particular, a wide variety of techniques like summability kernels, theory of entire functions, Gaussian cylindrical measures, approximation theory, Laguerre and Legendre polynomials are needed to analyze different properties of the Volterra operator. We also include a characterization of the commutator of the Volterra operator acting on L-P[0, 1], 1

Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map

We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x) = integral a(x, y) f(b( x, y)) mu(dy) acting on functions f: [u, v] --> C ( evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius-Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set C\(-infinity, 1]. Analyzing the spectrum of the Frobenius Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Ropstorff asymptotic formula for the decay of correlations of the Gauss map.

Time operator for diffusion

Volume: 11 Issue: 4 Pages: 465-477 Published: MAR 2000 Times Cited: 9 References: 15 Citation MapCitation Map beta Abstract: We extend the concept of time operator for general semigroups and construct a non-self-adjoint time operator for the diffusion equation which is intertwined with the unilateral shift. We obtain the spectral resolution, the age eigenstates and a new shift representation of the solution of the diffusion equation. Based on previous work we obtain similarly a self-adjoint time operator for Relativistic Diffusion. (C) 2000 Elsevier Science Ltd. All rights reserved.

The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.

A Context-Dependent Algorithm for Merging Uncertain Information in Possibility Theory

The need to merge multiple sources of uncertaininformation is an important issue in many application areas,especially when there is potential for contradictions betweensources. Possibility theory offers a flexible framework to represent,and reason with, uncertain information, and there isa range of merging operators, such as the conjunctive anddisjunctive operators, for combining information. However, withthe proposals to date, the context of the information to be mergedis largely ignored during the process of selecting which mergingoperators to use. To address this shortcoming, in this paper,we propose an adaptive merging algorithm which selects largelypartially maximal consistent subsets (LPMCSs) of sources, thatcan be merged through relaxation of the conjunctive operator, byassessing the coherence of the information in each subset. In thisway, a fusion process can integrate both conjunctive and disjunctiveoperators in a more flexible manner and thereby be morecontext dependent. A comparison with related merging methodsshows how our algorithm can produce a more consensual result.

Stable isomorphism of dual operator spaces

We prove that two dual operator spaces $X$ and $Y$ are stably isomorphic if and only if there exist completely isometric normal representations $phi$ and $psi$ of $X$ and $Y$, respectively, and ternary rings of operators $M_1, M_2$ such that $phi (X)= [M_2^*psi (Y)M_1]^{-w^*}$ and $psi (Y)=[M_2phi (X)M_1^*].$ We prove that this is equivalent to certain canonical dual operator algebras associated with the operator spaces being stably isomorphic. We apply these operator space results to prove that certain dual operator algebras are stably isomorphic if and only if they are isomorphic. We provide examples motivated by CSL algebra theory.

On the limits of spectral methods for frequency estimation

An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicates the intrinsic limitations of spectral methods when it comes to the task of measuring frequencies. Other examples, one from medicine and one from bifurcation theory, are given, which also exhibit these limitations of spectral methods. For two methods of spectral estimation it is verified that the particular way end points are treated, which is specific to each method, is, for long enough time series, not relevant for the main result.

Exact theory for localized envelope modulated electrostatic wavepackets in space and dusty plasmas

Abundant evidence for the occurrence of modulated envelope plasma wave packets is provided by recent satellite missions. These excitations are characterized by a slowly varying localized envelope structure, embedding the fast carrier wave, which appears to be the result of strong modulation of the wave amplitude. This modulation may be due to parametric interactions between different modes or, simply, to the nonlinear (self-)interaction of the carrier wave. A generic exact theory is presented in this study, for the nonlinear self-modulation of known electrostatic plasma modes, by employing a collisionless fluid model. Both cold (zero-temperature) and warm fluid descriptions are discussed and the results are compared. The (moderately) nonlinear oscillation regime is investigated by applying a multiple scale technique. The calculation leads to a Nonlinear Schrodinger-type Equation (NLSE), which describes the evolution of the slowly varying wave amplitude in time and space. The NLSE admits localized envelope (solitary wave) solutions of bright(pulses) or dark- (holes, voids) type, whose characteristics (maximum amplitude, width) depend on intrinsic plasma parameters. Effects like amplitude perturbation obliqueness (with respect to the propagation direction), finite temperature and defect (dust) concentration are explicitly considered. Relevance with similar highly localized modulated wave structures observed during recent satellite missions is discussed.

Operator hyperreflexivity of subspace lattices

We introduce and study the notion of operator hyperreflexivity of subspace lattices. This notion is a natural analogue of the operator reflexivity and is related to hyperreflexivity of subspace lattices introduced by Davidson and Harrison.

Operators, commuting with the Volterra operator, are not weakly supercyclic

We prove that any bounded linear operator on $L_p[0,1]$ for $1\leq p

Determination of the Tolman length in the improved Derjaguin-Broekhoff-de Boer theory for capillary condensation of ethanol in mesoporous thin films by ellipsometric porosimetry

Ethanol adsorption-desorption isotherms on well-organized mesoporous silica and titania films with hexagonal pores structure were studied by ellipsometric porosimetry. The mesopore volume Was calculated from the change of the effective refractive index at the end points of the isotherm. An improved Derjaguin-Broekhoff-de Boer (IDBdB) model for cylindrical pores is proposed for the determination of the pore size. In this model, the disjoining pressure isotherms were obtained by measuring the thickness of the ethanol film on a non-porous film with the same chemical composition. This approach eliminates uncertainties related to the application of the statistical film thickness determined via t-plots in previous versions of the DBdB model. The deviation in the surface tension of ethanol in the mesopores from that of a flat interface was described by the Tolman parameter in the Gibbs-Tolman-Koening-Buff equation. A positive value of the Tolman parameter of 0.2 nm was found from the fitting of the desorption branch of the isotherms to the experimental data obtained by Low Angle X-ray Diffraction (LA-XRD) and Transmission Electron Microscopy (TEM) measurements in the range of pore diameters between 2.1 and 8.3 nm. (C) 2009 Elsevier Inc. All rights reserved.

Theory of pixel lensing towards M31 - I. The density contribution and mass of MACHOs

POINT-AGAPE is an Angle-French collaboration which is employing the Isaac Newton Telescope (INT) to conduct a pixel-lensing survey towards M31. Pixel lensing is a technique which permits the detection of microlensing against unresolved stellar fields. The survey aims to constrain the stellar population in M31, and also the distribution and nature of massive compact halo objects (MACHOs) in both M31 and the Galaxy.

Detection of Voigt Spectral Line Profiles of Hydrogen Radio Recombination Lines toward Sagittarius B2(N)

We report the detection of Voigt spectral line profiles of radio recombination lines (RRLs) toward Sagittarius B2(N) with the 100 m Green Bank Telescope (GBT). At radio wavelengths, astronomical spectra are highly populated with RRLs, which serve as ideal probes of the physical conditions in molecular cloud complexes. An analysis of the Hn alpha lines presented herein shows that RRLs of higher principal quantum number (n > 90) are generally divergent from their expected Gaussian profiles and, moreover, are well described by their respective Voigt profiles. This is in agreement with the theory that spectral lines experience pressure broadening as a result of electron collisions at lower radio frequencies. Given the inherent technical difficulties regarding the detection and profiling of true RRL wing spans and shapes, it is crucial that the observing instrumentation produce flat baselines as well as high-sensitivity, high-resolution data. The GBT has demonstrated its capabilities regarding all of these aspects, and we believe that future observations of RRL emission via the GBT will be crucial toward advancing our knowledge of the larger-scale extended structures of ionized gas in the interstellar medium (ISM).

Quotients, exactness, and nuclearity in the operator system category

We continue our study of tensor products in the operator system category. We define operator system quotients and exactness in this setting and refine the notion of nuclearity by studying operator systems that preserve various pairs of tensor products. One of our main goals is to relate these refinements of nuclearity to the Kirchberg conjecture. In particular, we prove that the Kirchberg conjecture is equivalent to the statement that every operator system that is (min,er)-nuclear is also (el,c)-nuclear. We show that operator system quotients are not always equal to the corresponding operator space quotients and then study exactness of various operator system tensor products for the operator system quotient. We prove that an operator system is exact for the min tensor product if and only if it is (min,el)-nuclear. We give many characterizations of operator systems that are (min,er)-nuclear, (el,c)-nuclear, (min,el)-nuclear and (el,max)-nuclear. These characterizations involve operator system analogues of various properties from the theory of C*-algebras and operator spaces, including the WEP and LLP.