Spectral and Scattering Theory

ISBN-13: 9781489915542 / Angielski / Miękka / 2013 / 208 str.

Alexander G. Ramm

Opis

In this volume selected papers delivered at the special session on "Spectral and scattering theory" are published. This session was organized by A. G. Ramm at the first international congress ofISAAC (International Society for Analysis, Applications and Computing) which was held at the University of Delaware, June 3-7, 1997. The papers in this volume deal with a wide va- riety of problems including some nonlinear problems (Schechter, Trenogin), control theory (Shubov), fundamental problems of physics (Kitada), spectral and scattering theory in waveg- uides and shallow ocean (Ramm and Makrakis), inverse scattering with incomplete data (Ramm), spectral theory for Sturm-Liouville operators with singular coefficients (Yurko) and with energy-dependent coefficients (Aktosun, Klaus, and van der Mee), spectral theory of SchrOdinger operators with periodic coefficients (Kuchment, Vainberg), resolvent estimates for SchrOdinger-type and Maxwell's operators (Ben-Artzi and Nemirovsky), SchrOdinger oper- ators with von Neumann-Wignertype potentials (Rejto and Taboada), principal eigenvalues for indefinite-weight elliptic operators (pinchover), and symmetric solutions of Ginzburg-Landau equations (Gustafson). These papers will be of interest to a wide audience including mathematicians, physicists, and theoretically oriented engineers. A. G. Ramm Manhattan, KS v CONTENTS 1. Wave Scattering in 1-0 Nonconservative Media . . . . . . . . . . . . . . . . . . . Tuncay Aktosun, Martin Klaus, and Comelis van der Mee 2. Resolvent Estimates for SchrOdinger-type and Maxwell Equations with Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Matania Ben-Artzi and Jonathan Nemirovsky 3. Symmetric Solutions of Ginzburg-Landau Equations 33 S. Gustafson 4. Quantum Mechanics and Relativity: Their Unification by Local Time . . . . . . . 39 Hitoshi Kitada 5.

Spis treści

Wave Scattering in 1-D Nonconservative Media; T. Aktosun, et al. Resolvent Estimates for Schrödinger-type and Maxwell Equations with Applications; M. Ben-Artzi, J. Nemirovsky. Symmetric Solutions of Ginzburg-Landau Equations; S. Gustafson. Quantum Mechanics and Relativity: Their Unification by Local Time; H. Kitada. On Embedded Eigenvalues of Perturbed Periodic Schrödinger Operators; P. Kuchment, B. Vainberg. On Principal Eigenvalues for Indefinite-Weight Elliptic Problems; Y. Pinchover. Scattering by Obstacles in Acoustic Waveguides; A.G. Ramm, G.N. Makrakis. Recovery of Compactly Supported Spherically Symmetric Potentials from the Phase Shift of the s-Wave; A.G. Ramm. A Turning Point Problem Arising in Connection with a Limiting Absorption Principle for Schrödinger Operators with Generalized Von Neumann-Wigner Potentials; P. Rejto, M. Taboada. Eigenvalue Problems for Semilinear Equations; M. Schechter. Spectral Operators Generated by 3-Dimensional Damped Wave Equation and Applications to Control Theory; M.A. Shubov. Invertibility of Nonlinear Operators and Parameter Continuation Method; V.A. Trenogin. Sturm-Liouville Differential Operators with Singularities; V.Yurko. Index.