Resolvent and spectrum for discrete symplectic systems in the limit point case

Petr Zemánek

doi:10.1016/j.laa.2021.11.001

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arXiv · 2412.16756

Resolvent and spectrum for discrete symplectic systems in the limit point case

Petr Zemánek

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Abstract

The spectrum of an arbitrary self-adjoint extension of the minimal linear relation associated with the discrete symplectic system in the limit point case is completely characterized by using the limiting Weyl--Titchmarsh $M_+(\lambda)$-function. Furthermore, a dependence of the spectrum on a boundary condition is investigated and, consequently, several results of the singular Sturmian theory are derived.

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Petr Zemánek. 2024-12-21. Resolvent and spectrum for discrete symplectic systems in the limit point case. https://doi.org/10.1016/j.laa.2021.11.001

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