Uniformly bounded Riesz bases and equiconvergence theorems

Uniformly bounded Riesz bases and equiconvergence theorems

We review some classical results on the convergence of classical trigonometric and polynomial Fourier series. Then we present a not well-known short proof of the local uniform boundedness of many classical orthonormal systems. Finally, we formulate a strong generalization of Haar's classical eq...

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Bibliographic Details
Main Author: Vilmos Komornik
Format: Article
Language:English
Published: Sociedade Brasileira de Matemática 2007-11-01
Series:Boletim da Sociedade Paranaense de Matemática
Subjects:
Fourier Series
Riesz basis
classical orthogonal polynomials.
Online Access:http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/7430/4273
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spelling doaj-64e0ffda43b04dcdabc8ad698af142402020-11-25T00:00:33ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882007-11-01251-2139146Uniformly bounded Riesz bases and equiconvergence theoremsVilmos KomornikWe review some classical results on the convergence of classical trigonometric and polynomial Fourier series. Then we present a not well-known short proof of the local uniform boundedness of many classical orthonormal systems. Finally, we formulate a strong generalization of Haar's classical equiconvergence theorem.http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/7430/4273Fourier SeriesRiesz basisclassical orthogonal polynomials.
collection DOAJ
language English
format Article
sources DOAJ
author Vilmos Komornik
spellingShingle Vilmos Komornik
Uniformly bounded Riesz bases and equiconvergence theorems
Boletim da Sociedade Paranaense de Matemática
Fourier Series
Riesz basis
classical orthogonal polynomials.
author_facet Vilmos Komornik
author_sort Vilmos Komornik
title Uniformly bounded Riesz bases and equiconvergence theorems
title_short Uniformly bounded Riesz bases and equiconvergence theorems
title_full Uniformly bounded Riesz bases and equiconvergence theorems
title_fullStr Uniformly bounded Riesz bases and equiconvergence theorems
title_full_unstemmed Uniformly bounded Riesz bases and equiconvergence theorems
title_sort uniformly bounded riesz bases and equiconvergence theorems
publisher Sociedade Brasileira de Matemática
series Boletim da Sociedade Paranaense de Matemática
issn 0037-8712
2175-1188
publishDate 2007-11-01
description We review some classical results on the convergence of classical trigonometric and polynomial Fourier series. Then we present a not well-known short proof of the local uniform boundedness of many classical orthonormal systems. Finally, we formulate a strong generalization of Haar's classical equiconvergence theorem.
topic Fourier Series
Riesz basis
classical orthogonal polynomials.
url http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/7430/4273
work_keys_str_mv AT vilmoskomornik uniformlyboundedrieszbasesandequiconvergencetheorems
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