Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917876164722688 |
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| author | Zemánek, Petr |
| author_facet | Zemánek, Petr |
| contents | Eigenfunctions expansion for discrete symplectic systems on a finite discrete interval is established in the case of a general linear dependence on the spectral parameter as a significant generalization of the Expansion theorem given by Bohner, Došlý and Kratz in [Trans. Amer. Math. Soc. 361 (2009), 3109--3123]. Subsequently, an integral representation of the Weyl--Titchmarsh $M(λ)$-function is derived explicitly by using a suitable spectral function and a possible extension to the half-line case is discussed. The main results are illustrated by several examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16752 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Zemánek, Petr Spectral Theory Classical Analysis and ODEs 47B39, 39A12, 39A06, 34L10 Eigenfunctions expansion for discrete symplectic systems on a finite discrete interval is established in the case of a general linear dependence on the spectral parameter as a significant generalization of the Expansion theorem given by Bohner, Došlý and Kratz in [Trans. Amer. Math. Soc. 361 (2009), 3109--3123]. Subsequently, an integral representation of the Weyl--Titchmarsh $M(λ)$-function is derived explicitly by using a suitable spectral function and a possible extension to the half-line case is discussed. The main results are illustrated by several examples. |
| title | Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter |
| topic | Spectral Theory Classical Analysis and ODEs 47B39, 39A12, 39A06, 34L10 |
| url | https://arxiv.org/abs/2412.16752 |