Herglotz representation for operator-valued function on a set associated with test functions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909399613702144 |
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| author | Bhowmik, Mainak Kumar, Poornendu |
| author_facet | Bhowmik, Mainak Kumar, Poornendu |
| contents | The Herglotz representation theorem for holomorphic functions with non-negative real part is a fundamental result in the theory of holomorphic functions. In this paper, we reinterpret the Herglotz representation in the context of modern techniques, specifically realization formula. This reinterpretation is then extended to operator-valued functions on arbitrary sets, in association with a collection of test functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14455 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Herglotz representation for operator-valued function on a set associated with test functions Bhowmik, Mainak Kumar, Poornendu Functional Analysis Complex Variables 47A48, 47A56, 32A38 The Herglotz representation theorem for holomorphic functions with non-negative real part is a fundamental result in the theory of holomorphic functions. In this paper, we reinterpret the Herglotz representation in the context of modern techniques, specifically realization formula. This reinterpretation is then extended to operator-valued functions on arbitrary sets, in association with a collection of test functions. |
| title | Herglotz representation for operator-valued function on a set associated with test functions |
| topic | Functional Analysis Complex Variables 47A48, 47A56, 32A38 |
| url | https://arxiv.org/abs/2411.14455 |