Inverse Problems In The Theory Of Small Oscillations
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Inverse Problems in the Theory of Small Oscillations
Author: Vladimir Marchenko
language: en
Publisher: American Mathematical Soc.
Release Date: 2018-12-12
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.
Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems
Author: Feliks Ruvimovich Gantmakher
language: en
Publisher: American Mathematical Soc.
Release Date: 1961
The exposition is self-contained. The first chapter presents all necessary results (with proofs) on the theory of matrices which are not included in a standard linear algebra course. The only prerequisite in addition to standard linear algebra is the theory of linear integral equations used in Chapter 5. The book is suitable for graduate students, research mathematicians and engineers interested in ordinary differential equations, integral equations, and theirapplications.
Spectral Analysis, Differential Equations and Mathematical Physics: A Festschrift in Honor of Fritz Gesztesy's 60th Birthday
Author: Helge Holden
language: en
Publisher: American Mathematical Soc.
Release Date: 2013-07-08
This volume contains twenty contributions in the area of mathematical physics where Fritz Gesztesy made profound contributions. There are three survey papers in spectral theory, differential equations, and mathematical physics, which highlight, in particu