Weil-Titchmarsh theory as applied to the singular non-sectorial Schrödinger operator. Conditions for discreteness of the spectrum and compactness of the resolvent

2023/07/09 by Tumanov, Sergey N.
#34B09 #34B20 #34L05 #47E05 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2307.05559

Abstract

The spectral properties of the singular Schrödinger operator with complex-valued potential which takes values in a wider region than the half-plane, have been little studied. In general case, the operator is non-sectorial, and the numerical range coincides with the entire complex plane. In this situation we propose sufficient conditions for discreteness of the spectrum and compactness of the resolvent.

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