On the Reconstruction of a String from Spectral Data
作者:
Matthias Weber,
期刊:
Mathematische Nachrichten
(WILEY Available online 1999)
卷期:
Volume 197,
issue 1
页码: 135-156
ISSN:0025-584X
年代: 1999
DOI:10.1002/mana.19991970109
出版商: WILEY‐VCH Verlag
关键词: Vibrating string;inverse eigenvalue problem;Krein's correspondence;moment problems
数据来源: WILEY
摘要:
AbstractWe consider the problem to reconstruct the mass distribution of a string where the mass is concentrated in a finite number of points, or, equivalently, the problem to reconstruct a simply connected mass spring system with unknown masses and stiffness parameters if the following data are given.Problem 1: The spectra of the string and of a modification of the string, or.Problem 2: The spectra of two different modifications of the string.Here a modification of the string is a string which appears if we link the unknown string with another string of known mass distribution.The paper contains a necessary condition for the existence of a solution of Problem 1, and explicit formulas and an algorithm for the solutions of the Problems 1 and 2 under the condition that there exists a solution.For the case that the mass distribution of the unknown string is not discrete we consider the problem to find discrete approximations of this distribution from the respective spectral data.The methods are based on the spectral theory of generalized second order differential operators as developed by M. G. Krein
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