Wavelet transform, Toeplitz type operators and decomposition of functions on the upper half-plane
In this paper we consider the decomposition of functions on the upper half-plane into orthogonal subspaces which are isometric to \(L^{2}(\mathbb{R})\) by continuous wavelet transforms. A necessary and sufficient condition for such a decomposition is given. From such a decomposition by general Lagu...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
1992-02-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/448 |
| _version_ | 1828542748201844736 |
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| author | Ding-Xuan Zhou |
| author_facet | Ding-Xuan Zhou |
| author_sort | Ding-Xuan Zhou |
| collection | DOAJ |
| description |
In this paper we consider the decomposition of functions on the upper half-plane into orthogonal subspaces which are isometric to \(L^{2}(\mathbb{R})\) by continuous wavelet transforms. A necessary and sufficient condition for such a decomposition is given. From such a decomposition by general Laguerre polynomials, we define a series of Toeplitz type operators and study the Schatten-Von Neumann classes of these operators.
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| first_indexed | 2024-12-12T02:02:23Z |
| format | Article |
| id | doaj.art-3a4427dba26e4ef1bc003a417a752777 |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-12-12T02:02:23Z |
| publishDate | 1992-02-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-3a4427dba26e4ef1bc003a417a7527772022-12-22T00:42:08ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X1992-02-01211Wavelet transform, Toeplitz type operators and decomposition of functions on the upper half-planeDing-Xuan Zhou0Zhejiang University, China In this paper we consider the decomposition of functions on the upper half-plane into orthogonal subspaces which are isometric to \(L^{2}(\mathbb{R})\) by continuous wavelet transforms. A necessary and sufficient condition for such a decomposition is given. From such a decomposition by general Laguerre polynomials, we define a series of Toeplitz type operators and study the Schatten-Von Neumann classes of these operators. https://www.ictp.acad.ro/jnaat/journal/article/view/448continuous wavelet transformfunction spacesToeplitz type operatorsSchatten-Von Neumann classBesov spaces |
| spellingShingle | Ding-Xuan Zhou Wavelet transform, Toeplitz type operators and decomposition of functions on the upper half-plane Journal of Numerical Analysis and Approximation Theory continuous wavelet transform function spaces Toeplitz type operators Schatten-Von Neumann class Besov spaces |
| title | Wavelet transform, Toeplitz type operators and decomposition of functions on the upper half-plane |
| title_full | Wavelet transform, Toeplitz type operators and decomposition of functions on the upper half-plane |
| title_fullStr | Wavelet transform, Toeplitz type operators and decomposition of functions on the upper half-plane |
| title_full_unstemmed | Wavelet transform, Toeplitz type operators and decomposition of functions on the upper half-plane |
| title_short | Wavelet transform, Toeplitz type operators and decomposition of functions on the upper half-plane |
| title_sort | wavelet transform toeplitz type operators and decomposition of functions on the upper half plane |
| topic | continuous wavelet transform function spaces Toeplitz type operators Schatten-Von Neumann class Besov spaces |
| url | https://www.ictp.acad.ro/jnaat/journal/article/view/448 |
| work_keys_str_mv | AT dingxuanzhou wavelettransformtoeplitztypeoperatorsanddecompositionoffunctionsontheupperhalfplane |