Inverse Problems in the Theory of Small Oscillations

Victor Slavin, Vladimir Marchenko

ISBN 10: 1470448904 / ISBN 13: 9781470448905

Published by American Mathematical Society, US, 2018

About this Item

Inverse problems of spectral analysis deal with the reconstruction of operators of the specified form in Hilbert or Banach spaces from certain of their spectral characteristics. An interest in spectral problems was initially inspired by quantum mechanics. The main inverse spectral problems have been solved already for Schrodinger operators and for their finite-difference analogues, Jacobi matrices.This book treats inverse problems in the theory of small oscillations of systems with finitely many degrees of freedom, which requires finding the potential energy of a system from the observations of its oscillations. Since oscillations are small, the potential energy is given by a positive definite quadratic form whose matrix is called the matrix of potential energy. Hence, the problem is to find a matrix belonging to the class of all positive definite matrices. This is the main difference between inverse problems studied in this book and the inverse problems for discrete analogues of the Schrodinger operators, where only the class of tridiagonal Hermitian matrices are considered.

Seller Inventory # LU-9781470448905

Bibliographic Details

• Title: Inverse Problems in the Theory of Small Oscillations
• Publisher: American Mathematical Society, US
• Publication Date: 2018
• Language: English
• ISBN 10: 1470448904
• ISBN 13: 9781470448905
• Binding: Hardback
• Condition: New
• Weight: 448 grams

About this title

Synopsis

Inverse problems of spectral analysis deal with the reconstruction of operators of the specified form in Hilbert or Banach spaces from certain of their spectral characteristics. An interest in spectral problems was initially inspired by quantum mechanics. The main inverse spectral problems have been solved already for Schrödinger operators and for their finite-difference analogues, Jacobi matrices. This book treats inverse problems in the theory of small oscillations of systems with finitely many degrees of freedom, which requires finding the potential energy of a system from the observations of its oscillations. Since oscillations are small, the potential energy is given by a positive definite quadratic form whose matrix is called the matrix of potential energy. Hence, the problem is to find a matrix belonging to the class of all positive definite matrices. This is the main difference between inverse problems studied in this book and the inverse problems for discrete analogues of the Schrödinger operators, where only the class of tridiagonal Hermitian matrices are considered.