Infinite strings with discrete spectrum
\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.
scientific article; zbMATH DE number 4663