On the spectral properties of non-selfadjoint discrete Schr\"odinger operators

Olivier Bourget; Diomba Sambou; Amal Taarabt

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arXiv · 1807.01282

On the spectral properties of non-selfadjoint discrete Schr\"odinger operators

Olivier Bourget·Diomba Sambou·Amal Taarabt

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Abstract

Let $H_0$ be a purely absolutely continuous selfadjoint operator acting on some separable infinite-dimensional Hilbert space and $V$ be a compact non-selfadjoint perturbation. We relate the regularity properties of $V$ to various spectral properties of the perturbed operator $H_0+V$. The structure of the discrete spectrum and the embedded eigenvalues are analysed jointly with the existence of limiting absorption principles in a unified framework. Our results are based on a suitable combination of complex scaling techniques, resonance theory and positive commutators methods. Various results scattered throughout the literature are recovered and extended. For illustrative purposes, the case of the one-dimensional discrete Laplacian is emphasized.

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BibTeX RIS

Olivier Bourget, Diomba Sambou, Amal Taarabt. 2018-07-03. On the spectral properties of non-selfadjoint discrete Schr\"odinger operators. https://arxiv.org/abs/1807.01282

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