Thaís Jordão

• Abstract

  The main interest of this project is to study the relation of generalized Besov spaces and the decay of integral Fourier transformations (F-transformations). In particular, it aims to obtain Titchmarsh-type theorems for integral transformations with oscillating kernels. In this sense, generalized Besov spaces have been used recently to quantify the decay of the Fourier transform, either p…

  Decay of F-transforms and generalized Besov spaces, AP.R

• Abstract

  Function spaces of generalized smoothness (standard and generalized ones) were employed in order to quantify the decay of the Fourier transform, point-wise or through averages, and to express it naturally in terms of the original function. A characterization of functions in the generalized Besov and Lipschitz spaces in terms of decay properties of the Fourier transform was also obtained i…

  Embeddings of functions spaces of generalized smoothness, AP.R

• Abstract

  The main goal of this project refers to characterizations of K-funcionals (with fractional order) defined for functions on the euclidian space and on unit sphere. First of all such characterization is intended to be via a new average operator given by a convolution between a distribution and certain dilations of usual Lebesgue measure induced on the sphere. (AU)

  Characterizations of fractional order K-functionals and its applications, AP.R

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

• Abstract

  This project is based on exploring fundamental concepts of Functional Analysis and Advanced Calculus, through the concept of reproducing Hilbert spaces and functions defined on the unit sphere of Euclidean space, respectively. The objective is to develop the necessary mathematical background to understand the working environment involved in the search for estimates of epsilon-entropy of K…

  Reproducing Kernel Hilbert Spaces of Spherical Functions, BP.IC

• Abstract

  This project aims to present key concepts related to machine learning to the student, with emphasis on its mathematical foundations so that concepts directly linked to functional analysis and its subareas can be explored.

  Machine Learning: Theoretical fundamentation through function spaces, BP.IC

• Abstract

  This project is based on exploring fundamental concepts of analysis, in particular the study of functions spaces and operators, from the view of real functions. The objective is to develop with the student basic ideas of functional analysis in the context of real analysis and containing elements of Approximation Theory. This approach, directed to the supervisor's specialty, isn't covered …

  An approach to functional analysis by real functions, integral equations and Hilbert spaces, BP.IC

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

• Abstract

  The main goal of this project refers to characterizations of K-functionals (with fractional orders) on a general setting: compact two-point homogeneous space of rank one. Characterizations of this nature are highly important in Approximation Theory, where one of the most important problem is to feature the best approximation of a function by more simple functions (in the meaning of smooth…

  K-functionals of fractional orders and moduli of smoothness on a general setting, BE.PQ

• 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