Counting eigenvalues of Schr\"odinger operator with complex fast decreasing potential
Classical Analysis and ODEs
2019-02-07 v4 Complex Variables
Spectral Theory
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.
Cite
@article{arxiv.1811.05591,
title = {Counting eigenvalues of Schr\"odinger operator with complex fast decreasing potential},
author = {Alexander Borichev and Rupert Frank and Alexander Volberg},
journal= {arXiv preprint arXiv:1811.05591},
year = {2019}
}
Comments
29 pages; this version is a considerable improvement over the previous versions