A generalization of Krein`s extension formalism for symmetric relations with deficiency index (1,1)
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910718626889728 |
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| author | Emmel, Christian |
| author_facet | Emmel, Christian |
| contents | Let S be a symmetric relation with deficiency index (1,1). In this article, we extend Krein`s resolvent formalism in order to describe all, not necessarily self-adjoint, extensions $S \subset \tilde{A}$ with $\varrho(\tilde{A})\neq \emptyset$. The corresponding $Q$-functions turn out to be quasi-Herglotz functions. We will use their structure to characterize the spectrum of such extensions. Finally, we also provide a model for such an extension on a reproducing kernel Hilbert space when $S$ is simple. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07491 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A generalization of Krein`s extension formalism for symmetric relations with deficiency index (1,1) Emmel, Christian Functional Analysis Let S be a symmetric relation with deficiency index (1,1). In this article, we extend Krein`s resolvent formalism in order to describe all, not necessarily self-adjoint, extensions $S \subset \tilde{A}$ with $\varrho(\tilde{A})\neq \emptyset$. The corresponding $Q$-functions turn out to be quasi-Herglotz functions. We will use their structure to characterize the spectrum of such extensions. Finally, we also provide a model for such an extension on a reproducing kernel Hilbert space when $S$ is simple. |
| title | A generalization of Krein`s extension formalism for symmetric relations with deficiency index (1,1) |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2407.07491 |