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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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2007-11-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/7430/4273 |
| _version_ | 1818502909486170112 |
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| author | Vilmos Komornik |
| author_facet | Vilmos Komornik |
| author_sort | Vilmos Komornik |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-10T21:16:42Z |
| format | Article |
| id | doaj.art-64e0ffda43b04dcdabc8ad698af14240 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-12-10T21:16:42Z |
| publishDate | 2007-11-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-64e0ffda43b04dcdabc8ad698af142402022-12-22T01:33:17ZengSociedade 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. |
| spellingShingle | Vilmos Komornik Uniformly bounded Riesz bases and equiconvergence theorems Boletim da Sociedade Paranaense de Matemática Fourier Series Riesz basis classical orthogonal polynomials. |
| title | 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_short | Uniformly bounded Riesz bases and equiconvergence theorems |
| title_sort | uniformly bounded riesz bases and equiconvergence theorems |
| 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 |