A note on spectral theory of integral-functional Volterra operators
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916199713996800 |
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| author | Sidorov, Denis |
| author_facet | Sidorov, Denis |
| contents | A concise overview of the spectral theory of integral-functional operators is provided. In the context of analysis, a technique is described for deriving solutions to equations involving operators in a closed form. A constructive theorem has been established, outlining a procedure for determining the eigenvalues and eigenfunctions of these operators. Based on this foundation, an analytical approach for generating solutions to a Volterra-type integro-functional inhomogeneous equation is proposed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07041 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on spectral theory of integral-functional Volterra operators Sidorov, Denis Dynamical Systems 45D05 45M05 A concise overview of the spectral theory of integral-functional operators is provided. In the context of analysis, a technique is described for deriving solutions to equations involving operators in a closed form. A constructive theorem has been established, outlining a procedure for determining the eigenvalues and eigenfunctions of these operators. Based on this foundation, an analytical approach for generating solutions to a Volterra-type integro-functional inhomogeneous equation is proposed. |
| title | A note on spectral theory of integral-functional Volterra operators |
| topic | Dynamical Systems 45D05 45M05 |
| url | https://arxiv.org/abs/2404.07041 |