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Operator Theory and Its Applications
Edited by: A. G. Ramm, Kansas State University, Manhattan, KS, P. N. Shivakumar, University of Manitoba, Winnipeg, MB, Canada, and A. V. Strauss, Ul'yanovsk Pedagogical University, Russia
A co-publication of the AMS and Fields Institute.
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Fields Institute Communications
2000; 574 pp; hardcover
Volume: 25
ISBN-10: 0-8218-1990-9
ISBN-13: 978-0-8218-1990-6
List Price: US$151
Member Price: US$120.80
Order Code: FIC/25
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This volume contains a selection of papers presented at an international conference on operator theory and its applications held in Winnipeg. The papers chosen for this volume are intended to illustrate that operator theory is the language of modern analysis and its applications. Together with the papers on the abstract operator theory are many papers on the theory of differential operators, boundary value problems, inverse scattering and other inverse problems, and on applications to biology, chemistry, wave propagation, and many other areas.

The volume is dedicated to the late A. V. Strauss, whose principal areas of research were spectral theory of linear operators in Hilbert spaces, extension theory for symmetric linear operators, theory of the characteristic functions and functional models of linear operators, and boundary value problems with boundary conditions depending on spectral parameter. The bibliography of publications by A. V. Strauss combined with the papers from the conference provide both historical perspective and contemporary research on the field of operator theory and its applications.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

Mathematicians, engineers and graduate students interested in operator theory and its applications, PDEs, ordinary differential equations and quantum theory.

Table of Contents

  • A. Strauss -- Functional models of regular symmetric operators
  • A. G. Ramm -- Property C for ODE and applications to inverse problems
  • Ya. I. Alber -- Decomposition theorems in Banach spaces
  • R. Airapetyan -- On a new statement of inverse problem of quantum scattering theory
  • R. G. Airapetyan, A. G. Ramm, and A. B. Smirnova -- Continuous methods for solving nonlinear ill-posed problems
  • D. Alpay and Y. Peretz -- Quasi-coisometric realizations of upper triangular matrices
  • J. A. Ball -- Linear systems, operator model theory and scattering: Multivariable generalizations
  • J. A. Ball and N. J. Young -- Problems on the realization of functions
  • S. Belyi and E. Tsekanovskii -- Multiplication theorems for \(J\)-contractive operator-valued functions
  • Y. M. Berezansky -- Spectral theory of commutative Jacobi fields: Direct and inverse problems
  • G. F. Crosta -- The forward propagation method applied to the inverse obstacle problem of electromagnetics
  • J. Eisner and M. Kučera -- Spatial patterning in reaction-diffusion systems with nonstandard boundary conditions
  • A. Ětkin -- On an abstract boundary value problem with the eigenvalue parameter in the boundary condition
  • F. Gesztesy and K. A. Makarov -- Some applications of the spectral shift operator
  • S. Gutman and A. G. Ramm -- Application of the hybrid stochastic-deterministic minimization method to a surface data inverse scattering problem
  • W. Jäger and P. Rejto -- On a theorem of Mochizuki and Uchiyama about long range oscillating potentials I
  • V. Khatskevich and V. Senderov -- Basic properties of linear fractional mappings of operator balls: Schroeder's equation
  • E. Ya. Khruslov and L. S. Pankratov -- Homogenization of the Dirichlet variational problems in Orlicz-Sobolev spaces
  • B. V. Loginov, D. G. Rakhimov, and N. A. Sidorov -- Development of M. K. Gavurin's pseudoperturbation method
  • J. López-Gómez -- A bridge between operator theory and mathematical biology
  • M. Matvejchuk -- Measures on effects and on projections in spaces with indefinite metric
  • T. Nagai -- Concentration behavior of solutions to a chemotaxis system
  • R. Plato -- The solution of linear semidefinite ill-posed problems by the conjugate residual method
  • A. G. Ramm -- Justification of the limiting absorption principle in \(\mathbb R^2\)
  • A. G. Ramm -- Krein's method in inverse scattering
  • A. G. Ramm and M. Sammartino -- Existence and uniqueness of the scattering solutions in the exterior of rough domains
  • S. Ruan and J. C. Clements -- Existence and uniqueness of solutions of retarded quasilinear wave equations
  • E. I. Shifrin and B. Brank -- On solution of elliptical interface crack problem
  • A. Shklyar -- Some new effects for complete second order linear differential equations in Hilbert spaces
  • V. A. Trenogin -- Abstract boundary value problems for operator equations
  • A. V. Tsyganov -- On spectral decompositions of a restriction of a differential operator
  • N. N. Voitovich, Yu. P. Topolyuk, and O. O. Reshnyak -- Approximation of compactly supported functions with free phase by functions with bounded spectrum
  • A. Yagola and K. Dorofeev -- Sourcewise representation and a Posteriori error estimates for ill-posed problems
  • Y. Yamada -- Coexistence states for Lotka-Volterra systems with cross-diffusion
  • M. Yamaguchi and H. Yoshida -- Nonhomogeneous string problem with periodically moving boundaries
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