Vladimir Aleksandrovich Marchenko's Books

Sturm-Liouville Operators and Applications

By: Vladimir Aleksandrovich Marchenko

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Sturm-Liouville Operators and Applications

By: Vladimir Aleksandrovich Marchenko

The spectral theory of Sturm-Liouville operators is a classical domain of analysis, comprising a wide variety of problems. This book aims to show what can be achieved with the aid of transformation operators in spectral theory as well as their applications.

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Page Count

410

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821853163

ISBN 13

9780821853160

Spectral Operator Theory and Related Topics

By: Vladimir Aleksandrovich Marchenko

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Spectral Operator Theory and Related Topics

By: Vladimir Aleksandrovich Marchenko

The collection contains the papers of mathematicians who are participants of the seminar on Mathematical Physics in Kharkov, Ukraine. The papers are mainly devoted to nontraditional problems of spectral theory, of disordered systems, to the spectral aspects of homogenization, and of properties of ergodic dynamical systems."--ABSTRACT.

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Page Count

300

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082184122X

ISBN 13

9780821841228

Inverse Problems in the Theory of Small Oscillations

By: Vladimir Marchenko,Victor Slavin

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Inverse Problems in the Theory of Small Oscillations

By: Vladimir Marchenko,Victor Slavin

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.

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Page Count

170

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470448904

ISBN 13

9781470448905

Sturm-Liouville Operators and Applications

By: Vladimir Aleksandrovich Marchenko

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Sturm-Liouville Operators and Applications

By: Vladimir Aleksandrovich Marchenko

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Page Count

410

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821853163

ISBN 13

9780821853160

Determining Spectra in Quantum Theory

By: Michael Demuth,M. Krishna

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Determining Spectra in Quantum Theory

By: Michael Demuth,M. Krishna

This work focuses on various known criteria in the spectral theory of selfadjoint operators. The concise, unified presentation is aimed at graduate students and researchers working in the spectral theory of Schrodinger operators with either fixed or random potentials. But given the large gap this book fills in the literature, it will serve a wider audience of mathematical physicists in its contribution to works in spectral theory.

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Page Count

219

Publisher

Birkhäuser

Published Date

ISBN 10

0817643664

ISBN 13

9780817643669

Book's by Vladimir Aleksandrovich Marchenko

Sturm-Liouville Operators and Applications

Sturm-Liouville Operators and Applications

Spectral Operator Theory and Related Topics

Spectral Operator Theory and Related Topics

Inverse Problems in the Theory of Small Oscillations

Inverse Problems in the Theory of Small Oscillations

Sturm-Liouville Operators and Applications

Sturm-Liouville Operators and Applications

Determining Spectra in Quantum Theory

Determining Spectra in Quantum Theory

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