Operator Theory and Its Applications

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.

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