Spectral enclosures for non-self-adjoint discrete Schr\"odinger operators

Orif O. Ibrogimov; František Štampach

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arXiv · 1903.08620

Spectral enclosures for non-self-adjoint discrete Schr\"odinger operators

Orif O. Ibrogimov·František Štampach

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Abstract

We study location of eigenvalues of one-dimensional discrete Schr\"odinger operators with complex $\ell^{p}$-potentials for $1\leq p\leq \infty$. In the case of $\ell^{1}$-potentials, the derived bound is shown to be optimal. For $p>1$, two different spectral bounds are obtained. The method relies on the Birman-Schwinger principle and various techniques for estimations of the norm of the Birman-Schwinger operator.

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BibTeX RIS

Orif O. Ibrogimov, František Štampach. 2019-03-20. Spectral enclosures for non-self-adjoint discrete Schr\"odinger operators. https://arxiv.org/abs/1903.08620

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