Spectra of non-selfadjoint Hill's operators and a class of Riemann surfaces
type: Item
instance of: scholarly article
title: Spectra of non-selfadjoint Hill's operators and a class of Riemann surfaces
zbMATH Open document ID: 0856.34087
DOI: 10.2307/2118642
published in: Annals of Mathematics. Second Series
publication date: 1996-05-21T00:00:00Z
review text: The paper concerns a spectral analysis of the nonselfadjoint Hill's operator \(L= -{d^2\over dx^2}+ q\) in \(L^2(\mathbb{R})\) with scalar complex-valued \(\Pi\)-periodic function \(q\in L^2[0, \Pi]\). The spectrum \(\sigma(L)\) is formed by a countable system of analytic arcs. The aim of the paper is to describe all systems of analytic arcs which may be spectra of Hill's operators. The author shows that all possible spectra of Hill's operators are one-to-one parametrized by Riemann surfaces of a certain class.
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 34B30
zbMATH DE Number: 880143
zbMATH Keywords: spectral analysis
zbMATH Keywords: nonselfadjoint Hill's operator
author: Vadim Tkachenko
reviewed by: Teresa Regińska
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/2118642
OpenAlex ID: W2317860850
description: scientific article; zbMATH DE number 880143