Tropical varieties for non-archimedean analytic spaces

"Vegeu el resum a l'inici del document del fitxer adjunt."

Weighted Hardy spaces for the unit disc: approximation properties

In this paper we study basic properties of the weighted Hardy space for the unit disc with the weight function satisfying Muckenhoupt's (Aq) condition, and study related approximation problems (expansion, moment and interpolation) with respect to two incomplete systems of holomorphic functions in this space.

Norm inequalities in multidimensional Lorentz spaces

In this paper we obtain necessary and sufficient conditions for double trigonometric series to belong to generalized Lorentz spaces, not symmetric in general. Estimates for the norms are given in terms of coefficients.

Variational inequalities in Hilbert spaces with measures and optimal stopping problems

We study the existence theory for parabolic variational inequalities in weighted L2 spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L2 setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coeficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs.

On the boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures on metric spaces

In this paper we prove T1 type necessary and sufficient conditions for the boundedness on inhomogeneous Lipschitz spaces of fractional integrals and singular integrals defined on a measure metric space whose measure satisfies a n-dimensional growth. We also show that hypersingular integrals are bounded on these spaces.

Homotopy exponents for large H-Spaces

We show that H-spaces with finitely generated cohomology, as an algebra or as an algebra over the Steenrod algebra, have homotopy exponents at all primes. This provides a positive answer to a question of Stanley.

Net spaces and boundedness of integral operators

In this paper we introduce new functional spaces which we call the net spaces. Using their properties, the necessary and sufficient conditions for the integral operators to be of strong or weak-type are obtained. The estimates of the norm of the convolution operator in weighted Lebesgue spaces are presented.

Convolution inequalities in Lorentz spaces

In this paper we study boundedness of the convolution operator in different Lorentz spaces. In particular, we obtain the limit case of the Young-O'Neil inequality in the classical Lorentz spaces. We also investigate the convolution operator in the weighted Lorentz spaces. Finally, norm inequalities for the potential operator are presented.

Norm convolution inequalities in Lebesgue spaces

We obtain upper and lower estimates of the (p; q) norm of the con-volution operator. The upper estimate sharpens the Young-type inequalities due to O'Neil and Stepanov.

Bergman-type singular operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball

"Vegeu el resum a l'inici del document del fitxer adjunt."

Abstract splines in Krein spaces

"Vegeu el resum a l'inici del document del fitxer adjunt."

Research and teaching: a holy or an unholy alliance?

Much of the self-image of the Western university hangs on the idea that research and teaching are intimately connected. The central axiom here is that research and teaching are mutually supportive of each other. An institution lacking such a set of relationships between research and teaching falls short of what it means to be a university. This set of beliefs raises certain questions: Is it the case that the presence of such a mutually supportive set of relationships between research and teaching is a necessary condition of the fulfilment of the idea of the university? (A conceptual question). And is it true that, in practice today, such a mutually supportive set of relationships between research and teaching characterises universities? (An empirical question). In my talk, I want to explore these matters in a critical vein. I shall suggest that: a) In practice today, such a mutually supportive set of relationships between research and teaching is in jeopardy. Far from supporting each other, very often research and teaching contend against each other. Research and teaching are becoming two separate ideologies, with their own interest structures. b) Historically, the supposed tight link between research and teaching is both of recent origin and far from universally achieved in universities. Institutional separateness between research and teaching is and has been evident, both across institutions and even across departments in the same institution. c) Conceptually, research and teaching are different activities: each is complex and neither is reducible to the other. In theory, therefore, research and teaching may be said to constitute a holy alliance but in practice, we see more of an unholy alliance. If, then, in an ideal world, a positive relationship between research and teaching is still a worthwhile goal, how might it be construed and worked for? Seeing research and teaching as two discrete and unified sets of activity is now inadequate. Much better is a construal of research and teaching as themselves complexes, as intermingling pools of activity helping to form the liquid university that is emerging today. On this view, research and teaching are fluid spaces, ever on the move, taking up new shapes, and themselves dividing and reforming, as the university reworks its own destiny in modern society. On such a perspective, working out a productive relationship between research and teaching is a complex project. This is an alliance that is neither holy nor unholy. It is an uneasy alliance, with temporary accommodations and continuous new possibilities.

Interpolation methods for stochastic processes spaces

In this paper the scales of classes of stochastic processes are introduced. New interpolation theorems and boundedness of some transforms of stochastic processes are proved. Interpolation method for generously-monotonous rocesses is entered. Conditions and statements of interpolation theorems concern he xed stochastic process, which diers from the classical results.

Spaces with Noetherian cohomology

Is the cohomology of the classifying space of a p-compact group, with Noetherian twisted coefficients, a Noetherian module? This note provides, over the ring of p-adic integers, such a generalization to p-compact groups of the Evens-Venkov Theorem. We consider the cohomology of a space with coefficients in a module, and we compare Noetherianity over the field with p elements, with Noetherianity over the p-adic integers, in the case when the fundamental group is a finite p-group.

Hankel operators on holomorphic Hardy-Orlicz spaces

"Vegeu el resum a l'inici del document del fitxer adjunt."