Values at the positive integral points of the zeta-function of the Hill operator with a finite-zone potential
type: Item
instance of: scholarly article
title: Values at the positive integral points of the zeta-function of the Hill operator with a finite-zone potential
zbMATH Open document ID: 0593.34027
DOI: 10.1007/BF01076366
author: M. Vodzitskij
publication date: 1984-01-01T00:00:00Z
review text: Let \(L=-d^ 2/dx^ 2+g(x)\) be the Hill operator with finite-zone potential, \(S(1)=\{\lambda_ v\}\) the set of eigenvalues of the periodic boundary value problem for L, S(-1) the set of eigenvalues of the antiperiodic boundary value problem. The author gives explicit formulas for \(\zeta (k;L-w)= \sum'(\lambda_ v-w)^{-k}\) \((k=1,2,...)\), where \(w\in S(1)\cap S(-1)\) (\(\sum'\) denotes that the term with \(\lambda_ v=w\) is omitted in the case when \(w\in S(1)\).
Mathematics Subject Classification ID: 34L99
zbMATH DE Number: 3953279
zbMATH Keywords: second order differential equation
zbMATH Keywords: Hill operator
zbMATH Keywords: finite-zone potential
reviewed by: Alexandra Rodkina
MaRDI profile type: Publication
cites work: The spectrum of Hill's equation
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3953279