Hausdorff Operators on de Branges Spaces and Paley-Wiener spaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915903775440896 |
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| author | Mirotin, A. R. |
| author_facet | Mirotin, A. R. |
| contents | For a class of de Branges spaces containing polynomials, sufficient and necessary conditions are given for the boundedness and compactness of the Hausdorff operators under consideration. For the Paly-Wiener spaces we reduce the study of our Hausdorff operators to classical integral ones. The operators that appeared are Carleman and therefore closeble in $L^2(\mathbb{R})$. We obtain also conditions for boundedness, compactness and nuclearity of our operators in the Paley-Wiener space as well as the conditions for their belonging to the Hilbert-Schmidt class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01757 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hausdorff Operators on de Branges Spaces and Paley-Wiener spaces Mirotin, A. R. Functional Analysis Primary 47B91, Secondary 46E15, 30H20 For a class of de Branges spaces containing polynomials, sufficient and necessary conditions are given for the boundedness and compactness of the Hausdorff operators under consideration. For the Paly-Wiener spaces we reduce the study of our Hausdorff operators to classical integral ones. The operators that appeared are Carleman and therefore closeble in $L^2(\mathbb{R})$. We obtain also conditions for boundedness, compactness and nuclearity of our operators in the Paley-Wiener space as well as the conditions for their belonging to the Hilbert-Schmidt class. |
| title | Hausdorff Operators on de Branges Spaces and Paley-Wiener spaces |
| topic | Functional Analysis Primary 47B91, Secondary 46E15, 30H20 |
| url | https://arxiv.org/abs/2509.01757 |