Mathematical Scattering Theory

✍ Scribed by Prof. Dr. habil. Hellmut Baumgärtel, Dr. sc. Manfred Wollenberg (auth.)

• Publisher: Birkhäuser Basel
• Year: 1983
• Tongue: English
• Leaves: 448
• Series: Operator Theory: Advances and Applications 9
• Edition: 1
• Category: Library

✦ Synopsis

The aim of this book is to give a systematic and self-contained presentation of the Mathematical Scattering Theory within the framework of operator theory in Hilbert space. The term Mathematical Scattering Theory denotes that theory which is on the one hand the common mathematical foundation of several physical scattering theories (scattering of quantum objects, of classical waves and particles) and on the other hand a branch of operator theory devoted to the study of the behavior of the continuous part of perturbed operators (some authors also use the term Abstract Scattering Theory). EBBential contributions to the development of this theory are due to K. FRIEDRICHS, J. CooK, T. KATo, J. M. JAuCH, S. T. KURODA, M.S. BmMAN, M.G. KREiN, L. D. FAD­ DEEV, R. LAVINE, W. 0. AMREIN, B. SIMoN, D. PEARSON, V. ENss, and others. It seems to the authors that the theory has now reached a sufficiently developed state that a self-contained presentation of the topic is justified.

✦ Table of Contents

Front Matter....Pages 1-18
Introduction....Pages 19-24
Front Matter....Pages 25-25
Preliminaries....Pages 26-40
Multiplicity Theorie....Pages 41-44
Spectral Theory....Pages 45-66
Direct Integrals and Spectral Representations....Pages 67-79
Operator Spectral Integrals....Pages 80-93
Front Matter....Pages 95-96
General Theory of Asymptotic Constants....Pages 97-125
Special Classes of Asymptotic Constants....Pages 126-148
The Invariance of Wave Morphisms and Wave Algebras....Pages 149-167
Front Matter....Pages 169-169
Elementary Theory of Wave and Scattering Operators....Pages 170-194
Identifikation Operators....Pages 195-232
Structural Properties of Wave and Scattering Operators....Pages 233-249
Lax-Phillips Evolutions and Two-Space Wave Operators....Pages 250-263
Stationary Theory....Pages 264-291
Front Matter....Pages 299-300
Stationary methods....Pages 301-321
Time-Falloff Methods....Pages 322-342
Trace Class Methods....Pages 343-355
Smooth Perturbations....Pages 356-374
Front Matter....Pages 381-381
Representations of the Scattering Operator and the Scattering Amplitude, and Analyticity Properties of the Scattering Amplitude....Pages 382-399
Spectral Properties of the Scattering Amplitude....Pages 400-417
Back Matter....Pages 420-449

✦ Subjects

Science, general