Spectrum of multidimensional operators with periodic coefficients
type: Item
instance of: scholarly article
title: Spectrum of multidimensional operators with periodic coefficients
zbMATH Open document ID: 0566.47015
DOI: 10.1007/BF01077867
publication date: 1983-01-01T00:00:00Z
review text: Consider in \(L_ 2(R^ v)\) a selfadjoint operator H of the form \(H^ 0+Q\). Here \(H^ 0=J(i\partial /\partial x)\) is a differential or pseudo- differential operator with constant coefficients, J is a real-valued function, smooth except possibly at the point 0, satisfying \(J(tx)=| t|^ rJ(x),\) (t\(\in R\), \(r>0)\), \(J(x)>0\) for \(x\neq 0\) and an additional convexity condition. The operator Q is assumed to be bounded, selfadjoint and commuting with shifts by certain vectors. Assuming further the continuity of a certain mapping, the spectrum of H is continuous, and consists of a union of real closed intervals with lacunae between them. The paper presents conditions involving v and r that ensure that the number of the lacunae in the spectrum is finite.
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 47Gxx
zbMATH DE Number: 3903370
zbMATH Keywords: selfadjoint operator
zbMATH Keywords: pseudo-differential operator with constant coefficients
zbMATH Keywords: convexity
zbMATH Keywords: lacunae in the spectrum
author: M. M. Skriganov
MaRDI profile type: Publication
cites work: ON THE NUMBER OF LATTICE POINTS INSIDE A RANDOM OVAL
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3903370