Two weight inequalities for discrete positive operators

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Coefficients of Drinfeld modular forms and Hecke operators

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The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

Index theory for basic Dirac operators on Riemannian foliations

In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.

On slicewise monotone parameterized problems and optimal proof systems for TAUT

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Hankel operators on holomorphic Hardy-Orlicz spaces

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Complex and real Hausdorff operators

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Moduli of smoothness and rate of a.e. convergence for some convolution operators

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Folner sequences and finite operators

This article analyzes Folner sequences of projections for bounded linear operators and their relationship to the class of finite operators introduced by Williams in the 70ies. We prove that each essentially hyponormal operator has a proper Folner sequence (i.e. a Folner sequence of projections strongly converging to 1). In particular, any quasinormal, any subnormal, any hyponormal and any essentially normal operator has a proper Folner sequence. Moreover, we show that an operator is finite if and only if it has a proper Folner sequence or if it has a non-trivial finite dimensional reducing subspace. We also analyze the structure of operators which have no Folner sequence and give examples of them. For this analysis we introduce the notion of strongly non-Folner operators, which are far from finite block reducible operators, in some uniform sense, and show that this class coincides with the class of non-finite operators.

Implementació de la cerca d'un subgraf comú maximal a dos grafs mitjançant colles

La memòria que ací es presenta s'emmarca dins de l'àrea de teoria de grafs. En concret es treballa la implementació d'un algorisme per trobar el subgraf comú maximal (SCM) de dos grafs mitjançant la cerca de colles maximals (CM). L'aportació principal del projecte consisteix en, donats dos grafs qualsevol, trobar el seu graf associat per tal de poder cercar la seva colla maximal (CM). I així, utilitzant funcions existents en el llenguatge de programació, poder trobar el seu subgraf comú maximal (SCM), necessari per calcular la distància entre grafs i així determinar quan d'isomorfs són.

The equity core and the Lorenz-maximal allocations in the equal division core

In this paper, we characterize the non-emptiness of the equity core (Selten, 1978) and provide a method, easy to implement, for computing the Lorenz-maximal allocations in the equal division core (Dutta-Ray, 1991). Both results are based on a geometrical decomposition of the equity core as a finite union of polyhedrons. Keywords: Cooperative game, equity core, equal division core, Lorenz domination. JEL classification: C71

Hierachy-based methodology for producing educational contents with maximal reutilization

Computer based training or distance education are facing dramatic changes withthe advent of standardization efforts, some of them concentrating in maximal reuse.This is of paramount importance for a sustainable -cost affordable- production ofeducational materials. Reuse in itself should not be a goal, though, since manymethodological aspects might be lost. In this paper we propose two contentproduction approaches for the InterMediActor platform under a competence-basedmethodology: either a bottom-up approach where content is designed from scratchor a top-down methodology where existing material can be gradually adapted tofulfil requisites to be used with maximal flexibility into InterMediActor.