Infinite strings with discrete spectrum
type: Item
instance of: scholarly article
title: Infinite strings with discrete spectrum
zbMATH Open document ID: 0738.73056
DOI: 10.1007/BF01848990
published in: Periodica Mathematica Hungarica
publication date: 1992-06-25T00:00:00Z
review text: \textit{A. Bogmèr}, the author and \textit{I. Joó} [On the control of strings. A. Haar Mem. Conf. (Colloq. Math. Soc. Bolyai 49) North Holland, Amsterdam (1987)] considered the control problem of an infinite string with continuous spectrum. The aim of the present paper is to study the infinite strings with discrete spectrum. The author is indebted to B. M. Levitan who called his attention that the infinite string with discrete spectrum is an intermediate step between regular finite strings and infinite strings with continuous spectrum. The paper is organized in the following way. In \S1 we build up the background of the Fourier method which will be applied in \S2 where the existence and uniqueness of the solution of the string equation is given. Finally in \S3 control-theoretic results are obtained.
Mathematics Subject Classification ID: 74M05
Mathematics Subject Classification ID: 93C95
Mathematics Subject Classification ID: 74K05
zbMATH DE Number: 4663
zbMATH Keywords: Fourier method
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: approximate controllability
zbMATH Keywords: Riesz basis
author: Barnabás Apagyi
MaRDI profile type: Publication
cites work: Q4196846
cites work: Riesz bases of exponentials and sine-type functions
cites work: On control problems
cites work: A string equation with special boundary conditions
cites work: Vibrating strings with free ends
cites work: Q3807054
cites work: Q4746318
description: scientific article; zbMATH DE number 4663