Inverses of integral transforms of RKHSs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912170218881024 |
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| author | Yamada, Akira |
| author_facet | Yamada, Akira |
| contents | The Fourier transform and its inverse are well-known to have complex conjugate integral kernels. S.~Saitoh demonstrated that this relationship extends to the theory of integral transforms of Hilbert spaces of functions under certain conditions. In this paper, we derive a necessary and sufficient condition for the inverse of an integral transform of a Hilbert space of functions to be represented by a complex conjugate integral kernel. As an application, we present an alternative proof of Plancherel's theorem using the theory of reproducing kernels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19047 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inverses of integral transforms of RKHSs Yamada, Akira Functional Analysis Complex Variables The Fourier transform and its inverse are well-known to have complex conjugate integral kernels. S.~Saitoh demonstrated that this relationship extends to the theory of integral transforms of Hilbert spaces of functions under certain conditions. In this paper, we derive a necessary and sufficient condition for the inverse of an integral transform of a Hilbert space of functions to be represented by a complex conjugate integral kernel. As an application, we present an alternative proof of Plancherel's theorem using the theory of reproducing kernels. |
| title | Inverses of integral transforms of RKHSs |
| topic | Functional Analysis Complex Variables |
| url | https://arxiv.org/abs/2412.19047 |