A reproducing kernel approach to Lebesgue decomposition
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911121987862528 |
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| author | Bal, Jashan Martin, Robert T. W. Naderi, Fouad |
| author_facet | Bal, Jashan Martin, Robert T. W. Naderi, Fouad |
| contents | We show that properties of pairs of finite, positive and regular Borel measures on the complex unit circle such as domination, absolute continuity and singularity can be completely described in terms of containment and intersection of their reproducing kernel Hilbert spaces of `Cauchy transforms' in the complex unit disk. This leads to a new construction of the classical Lebesgue decomposition and proof of the Radon--Nikodym theorem using reproducing kernel theory and functional analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01961 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A reproducing kernel approach to Lebesgue decomposition Bal, Jashan Martin, Robert T. W. Naderi, Fouad Functional Analysis We show that properties of pairs of finite, positive and regular Borel measures on the complex unit circle such as domination, absolute continuity and singularity can be completely described in terms of containment and intersection of their reproducing kernel Hilbert spaces of `Cauchy transforms' in the complex unit disk. This leads to a new construction of the classical Lebesgue decomposition and proof of the Radon--Nikodym theorem using reproducing kernel theory and functional analysis. |
| title | A reproducing kernel approach to Lebesgue decomposition |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2312.01961 |