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arXiv · 1811.05591

Counting eigenvalues of Schr\"odinger operator with complex fast decreasing potential

Alexander Borichev·Rupert Frank·Alexander Volberg
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Abstract

We give a sharp estimate of the number of zeros of analytic functions in the unit disc belonging to analytic quasianalytic Carleman--Gevrey classes. As an application, we estimate the number of the eigenvalues for discrete Schr\"odinger operators with rapidly decreasing complex-valued potentials, and, more generally, for non-symmetric Jacobi matrices.

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Alexander Borichev, Rupert Frank, Alexander Volberg. 2018-11-14. Counting eigenvalues of Schr\"odinger operator with complex fast decreasing potential. https://arxiv.org/abs/1811.05591

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