**Fields Institute Communications**

Volume: 25;
2000;
574 pp;
Hardcover

MSC: Primary 47; 35; 34; 81;

Print ISBN: 978-0-8218-1990-6

Product Code: FIC/25

List Price: $159.00

AMS Member Price: $127.20

MAA member Price: $143.10

**Electronic ISBN: 978-1-4704-3049-8
Product Code: FIC/25.E**

List Price: $159.00

AMS Member Price: $127.20

MAA member Price: $143.10

# Operator Theory and Its Applications

Share this page *Edited by *
*A. G. Ramm; P. N. Shivakumar; A. V. Strauss*

A co-publication of the AMS and Fields Institute

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

## Operator Theory and Its Applications

- Cover Cover11
- Title page iii4
- Contents v6
- Preface ix10
- Dedication xi12
- Publications of Abraham V. Strauss xv16
- Functional models of regular symmetric operators 120
- Property C for ODE and applications to inverse problems 1534
- Decomposition theorems in Banach spaces 7796
- On a new statement of inverse problem of quantum scattering theory 95114
- Continuous methods for solving nonlinear ill-posed problems 111130
- Quasi-coisometric realizations of upper triangular matrices 139158
- Linear systems, operator model theory and scattering: Multivariable generalizations 151170
- Problems on the realization of functions 179198
- Multiplication theorems for 𝐽-contractive operator-valued functions 187206
- Spectral theory of commutative Jacobi fields: Direct and inverse problems 211230
- The forward propagation method applied to the inverse obstacle problem of electromagnetics 225244
- Spatial patterning in reaction-diffusion systems with nonstandard boundary conditions 239258
- On an abstract boundary value problem with the eigenvalue parameter in the boundary condition 257276
- Some applications of the spectral shift operator 267286
- Application of the hybrid stochastic-deterministic minimization method to a surface data inverse scattering problem 293312
- On a theorem of Mochizuki and Uchiyama about long range oscillating potentials I 305324
- Basic properties of linear fractional mappings of operator balls: Schroeder’s equation 331350
- Homogenization of the Dirichlet variational problems in Orlicz-Sobolev spaces 345364
- Development of M. K. Gavurin’s pseudoperturbation method 367386
- A bridge between operator theory and mathematical biology 383402
- Measures on effects and on projections in spaces with indefinite metric 399418
- Concentration behavior of solutions to a chemotaxis system 415434
- The solution of linear semidefinite ill-posed problems by the conjugate residual method 423442
- Justification of the limiting absorption principle in ℝ² 433452
- Krein’s method in inverse scattering 441460
- Existence and uniqueness of the scattering solutions in the exterior of rough domains 457476
- Existence and uniqueness of solutions of retarded quasilinear wave equations 473492
- On solution of elliptical interface crack problem 485504
- Some new effects for complete second order linear differential equations in Hilbert spaces 497516
- Abstract boundary value problems for operator equations 509528
- On spectral decompositions of a restriction of a differential operator 523542
- Approximation of compactly supported functions with free phase by functions with bounded spectrum 531550
- Sourcewise representation and a Posteriori error estimates for ill-posed problems 543562
- Coexistence states for Lotka-Volterra systems with cross-diffusion 551570
- Nonhomogeneous string problem with periodically moving boundaries 565584
- Back Cover Back Cover1594