On isospectral periodic potentials on a discrete lattice. I
type: Item
instance of: scholarly article
title: On isospectral periodic potentials on a discrete lattice. I
zbMATH Open document ID: 0696.35140
DOI: 10.1215/S0012-7094-88-05705-5
author: T. Kappeler
published in: Duke Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: The author studies the connection between potentials having the same spectrum with periodicity or crystal momentum conditions, when the space is a discrete lattice (this might correspond to a crystal equation after a proper discretization). He estimates the number of potentials having the same spectrum and gives more precise results when the difference operator is a discrete Laplacian.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35P99
Mathematics Subject Classification ID: 82D25
zbMATH DE Number: 4140369
zbMATH Keywords: isospectral periodic potentials
zbMATH Keywords: generalized Schrödinger equation
reviewed by: J. Frédéric Bonnans
MaRDI profile type: Publication
cites work: HANS BETHE'S CONTRIBUTIONS TO SOLID-STATE PHYSICS
cites work: On manifolds of negative curvature with isospectral potentials
cites work: On the compactness of ISO-spectral potentials
cites work: Isospectral deformations I: Riemannian structures on two-step nilspaces
cites work: Q3709254
cites work: On isospectral periodic potentials in Rn
cites work: Lectures on moduli of curves. Notes by D. R. Gokhale
cites work: Q3719440
cites work: Riemannian manifolds isospectral on functions but not on 1-forms
cites work: Isospectral deformations of compact solvmanifolds
cites work: The spectrum of the Laplacian on Riemannian Heisenberg manifolds
cites work: Isometry Groups of Riemannian Solvmanifolds
cites work: Spectral theory on S**2: some open questions
cites work: Some inverse spectral results for negatively curved 2-manifolds
cites work: Q3906160
cites work: On spherical spaces forms which are isospectral but not isometric
cites work: On isospectral potentials on a discrete lattice. II
cites work: The spectrum of Jacobi matrices
cites work: Q3915684
cites work: Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points
cites work: Riemannian coverings and isospectral manifolds
cites work: Isospectral and non-isometric Riemannian manifolds
full work available at URL: s0012-7094-88-05705-5
OpenAlex ID: W2072456128
description: scientific article; zbMATH DE number 4140369