A Survey on Reproducing Kernel Krein Spaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2013
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| _version_ | 1866914128047636480 |
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| author | Gheondea, Aurelian |
| author_facet | Gheondea, Aurelian |
| contents | This is a survey on reproducing kernel Krein spaces and their interplay with operator valued Hermitian kernels. Existence and uniqueness properties are carefully reviewed. The approach we follow in this survey uses a more abstract but very useful concept of linearization or Kolmogorov decomposition, as well as the underlying concept of Krein space induced by a selfadjoint operator and that of Krein space continuously embedded. The operator range feature of reproducing kernel spaces is emphasized. We include a careful presentation of Hermitian kernels on complex regions that points out a universality property of the Szego kernels with respect to reproducing kernel Krein spaces of holomorphic functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1309_2393 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | A Survey on Reproducing Kernel Krein Spaces Gheondea, Aurelian Functional Analysis 46C07, 46C20, 47B32, 47B50, 32A25 This is a survey on reproducing kernel Krein spaces and their interplay with operator valued Hermitian kernels. Existence and uniqueness properties are carefully reviewed. The approach we follow in this survey uses a more abstract but very useful concept of linearization or Kolmogorov decomposition, as well as the underlying concept of Krein space induced by a selfadjoint operator and that of Krein space continuously embedded. The operator range feature of reproducing kernel spaces is emphasized. We include a careful presentation of Hermitian kernels on complex regions that points out a universality property of the Szego kernels with respect to reproducing kernel Krein spaces of holomorphic functions. |
| title | A Survey on Reproducing Kernel Krein Spaces |
| topic | Functional Analysis 46C07, 46C20, 47B32, 47B50, 32A25 |
| url | https://arxiv.org/abs/1309.2393 |