Valdir Antonio Menegatto

• Abstract

  The principal objectives of this project are to study themes related to Harmonic Analysis, Approximation Theory and Special Functions and their Applications. Harmonic Analysis is a cornerstone of Analysis. The solutions of the principal partial differential equation are generally represented by convolutions and these representations are obtained via an application of the Fourier transform…

  Harmonic analysis, approximation theory and applications, AP.TEM

• Abstract

  Positive definite kernels and integral operators generated by them enter as important tools in the formulation of many problems in pure and applied mathematics. These problems intersect many research areas, including approximation theory, functional analysis, classical analysis, learning theory, etc. This proposal encompasses the resolution of problems aligned with the following topics: r…

  Positive definite kernels and integral operators generated by them, AP.R

• Abstract

  Integral operators are animportant tool in the formulation of several problems within pureand applied mathematics, for example, those in approximation theory,operator theory, classical analysis, learning theory, etc.\ Thisproject intends to consider some problems involving such operators,namely some related to Mercer's theory, reproducing kernel Hilbertspaces and eigenvalue decay, all ali…

  Analysis of integral operators generated by positive definite kernels, AP.R

(Only some records are available in English at this moment)

• Abstract

  This project seeks characterizations for positive definite and stritcly positive definite isotropic matrix-valued functions on (real and complex) spheres and other manifolds, similar to the classical characterization obtained by I. J. Schoenberg in the forties for scalar positive definite and stritcly positive definite isotropic functions on spheres.\ In the strict case the investigation …

  Positive definite functions on spheres: the matricial and parametrical versions, BP.DR

• Abstract

  This project is intended to address the analysis of some recent results on positive definite and bizonal kernels on the usual m-dimensional unit sphere. The analysis seeks a possible application in the characterization of those positive definite and bizonal kernels which are strictly positive definite of some fixed order. Actually, as some characterizations are already available, the mai…

  Strictly positive definite kernels on the sphere: an analysis of the recent results., BP.MS

• Abstract

  The project seeks decay rates for eigenvalues of integral operators generated by smooth kernels on the sphere. The intended analysis will be based on abstract Hölder assumptions on the generating kernel, taking into account existing decay rates with other Hölder conditions. (AU)

  Eigenvalues of integral operators generated by kernels satisfying abstract Hölder conditions, BP.PD

(Only some records are available in English at this moment)

• Abstract

  We intend to obtain sharp decay rates for eingenvalues of integral operators on the sphere when the generating kernel is positive definite and satisfies a Holder condition based on a family of operators defined by convolution with measures. (AU)

  Eigenvalues of integral operators generated by kernels satisfying a holder condition defined by spherical convolution, BE.EP.PD