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Spectral Operator Theory and Related Topics
Edited by: V. A. Marchenko

Advances in Soviet Mathematics
1994; 286 pp; hardcover
Volume: 19
ISBN-10: 0-8218-4122-X
ISBN-13: 978-0-8218-4122-8
List Price: US$129
Member Price: US$103.20
Order Code: ADVSOV/19
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This collection contains papers by participants in the Seminar on Mathematical Physics in Kharkov, Ukraine. The papers mainly focus on nontraditional problems of spectral theory, such as new types of inverse problems for one-dimensional differential operators, new classes of solutions to nonlinear differential equations obtained using spectral methods, distribution of eigenvalues of large random matrices, and related problems of statistical physics of disordered systems. In addition, the papers explore the spectral aspects of homogenization and of properties of ergodic dynamical systems. All the papers contain original results published for the first time.


Graduate students in mathematics and researchers in spectral theory, nonlinear equations, and disordered systems.

Table of Contents

  • D. S. Lundina and V. A. Marchenko -- Limits of the reflectionless Dirac operator
  • M. Novitskiĭ -- Quasianalytic classes and isospectral Hill's operators
  • V. A. Tkachenko -- Discriminants and generic spectra of nonselfadjoint Hill's operators
  • V. Ya. Golodets, A. I. Danilenko, and S. I. Bezuglyĭ -- On cocycles of ergodic dynamical systems and automorphisms compatible with them
  • A. M. Khorunzhy and L. A. Pastur -- On the eigenvalue distribution of the deformed Wigner ensemble of random matrices
  • E. Ya. Khruslov and V. P. Kotlyarov -- Soliton asymptotics of nondecreasing solutions of nonlinear completely integrable evolution equations
  • I. E. Egorova -- The Cauchy problem for the KdV equation with almost periodic initial data whose spectrum is nowhere dense
  • D. G. Shepel'sky -- The inverse problem of reconstruction of the medium's conductivity in a class of discontinuous and increasing functions
  • E. Khruslov and L. Pankratov -- Homogenization of boundary problems for the Ginzburg-Landau equation in weakly connected domains
  • B. Khoruzhenko, L. Pastur, and M. Shcherbina -- The infinite component limit of the random anisotropy \(n\)-vector model
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