Related papers: Some Topics in Fourier Analysis and Approximation …
A brief overview of publications in approximation theory of functions known to the author and connected with scientific publications by V.~K.~Dzyadyk (1919--1998).
The purpose of this seminar, which was presented at the Universitat Polit\`ecnica de Val\`encia in late 2012, is to explain several results concerning the bounded approximation property for Fr\'echet spaces. We give a full detailed proof of…
The area of Fourier analysis connected to signal processing theory has undergone a rapid development in the last two decades. The aspect of this development that has received the most publicity is the theory of wavelets and their relatives,…
This textbook is based on lectures given by the authors at MIPT (Moscow), HSE (Moscow), FEFU (Vladivostok), V.I. Vernadsky KFU (Simferopol), ASU (Republic of Adygea), and the University of Grenoble-Alpes (Grenoble, France). First of all,…
This is the material for two lectures given at Ecole Polytechnique in May 2011 for the math teachers of "classes pr\'eparatoires"(parallel to the undergraduate classes in universities). The introduction is a personal overview on Fourier…
Over the decades, Functional Analysis has been enriched and inspired on account of demands from neighboring fields, within mathematics, harmonic analysis (wavelets and signal processing), numerical analysis (finite element methods,…
The present informal set of notes covers the material that has been presented by the author in a series of lectures for the Doctoral School in Mathematics of the Southern Federal State University of Rostov-on-Don in the Fall of 2020 and…
Dunkl theory is a far reaching generalization of Fourier analysis and special function theory related to root systems. During the sixties and seventies, it became gradually clear that radial Fourier analysis on rank one symmetric spaces was…
The subject of this textbook is the analysis of Boolean functions. Roughly speaking, this refers to studying Boolean functions $f : \{0,1\}^n \to \{0,1\}$ via their Fourier expansion and other analytic means. Boolean functions are perhaps…
Contents of Part 1: 1. Status of the Standard Model(P.H. Frampton), 2. Cosmological Constraints from MBA and Polarization (A. Melchiorri), 3. AdS/CFT Correspondence and Unification at About 4 TeV (P.H. Frampton), 4. New Solutions in String…
Extending ideas of A.N. Parshin and D.V. Osipov, Harmonic Analysis is developed for filtered infinite dimensional modules over a ring. We establish Pontryagin duality, the Fourier inversion formula, Plancherel formula and Poisson summation…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. The second paper is concerned with simultaneous approximation to functions and their…
Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying Diophantine approximation in an arbitrary totally bounded metric space where the rationals are…
This paper develops a functional-analytic framework for approximating the push-forward induced by an analytic map from finitely many samples. Instead of working directly with the map, we study the push-forward on the space of locally…
Fourier Series is the second of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such as partial…
This book contains a large number of exercises related to different stochastic disciplines. Difficulty of the problems varies from the basic level in the first chapter up to the analysis of articles in Probability, Statistics and Computer…
Approximation theorem is one of the most important aspects of numerical analysis that has evolved over the years with many different approaches. Some of the most popular approximation methods include the Lebesgue approximation theorem, the…
This paper gives a short survey of some basic results related to estimates of fractional integrals and Fourier transforms. It is closely adjoint to our previous survey papers \cite{K1998} and \cite{K2007}. The main methods used in the paper…
This paper contains a transcript of my presentation at the Wyant Tribute Symposium on August 2, 2021 at SPIE's Optics & Photonics conference in San Diego, California. The technical part of the paper has no overlap with a previous article of…
This article, which grew out of my lecture at the conference "Analysis and Applications: A Conference in Honor of Elias M. Stein" in May 2011, is intended to give an overview on a collection of results which have been obtained jointly with…