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Mathematical Scattering Theory

  • Book
  • © 1983

Overview

Authors:
  1. Hellmut Baumgärtel

    1. Institut für Mathematik, Akademie der Wissenschaften der DDR, Deutschland

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  2. Manfred Wollenberg

    1. Institut für Mathematik, Akademie der Wissenschaften der DDR, Deutschland

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Operator Theory: Advances and Applications (OT, volume 9)

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Table of contents (20 chapters)

  1. Front Matter

    Pages 1-18
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  2. Introduction

    1. Introduction

      • Hellmut Baumgärtel, Manfred Wollenberg
      Pages 19-24

  3. Selfadjoint Operators in Hilbert Spaces

    1. Front Matter

      Pages 25-25
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    2. Preliminaries

      • Hellmut Baumgärtel, Manfred Wollenberg
      Pages 26-40

    3. Multiplicity Theorie

      • Hellmut Baumgärtel, Manfred Wollenberg
      Pages 41-44

    4. Spectral Theory

      • Hellmut Baumgärtel, Manfred Wollenberg
      Pages 45-66

    5. Direct Integrals and Spectral Representations

      • Hellmut Baumgärtel, Manfred Wollenberg
      Pages 67-79

    6. Operator Spectral Integrals

      • Hellmut Baumgärtel, Manfred Wollenberg
      Pages 80-93

  4. Algebras of Asymptotic Constants

    1. Front Matter

      Pages 95-96
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    2. General Theory of Asymptotic Constants

      • Hellmut Baumgärtel, Manfred Wollenberg
      Pages 97-125

    3. Special Classes of Asymptotic Constants

      • Hellmut Baumgärtel, Manfred Wollenberg
      Pages 126-148

    4. The Invariance of Wave Morphisms and Wave Algebras

      • Hellmut Baumgärtel, Manfred Wollenberg
      Pages 149-167

  5. Two-Space Wave Operators and Scattering Operators

    1. Front Matter

      Pages 169-169
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    2. Elementary Theory of Wave and Scattering Operators

      • Hellmut Baumgärtel, Manfred Wollenberg
      Pages 170-194

    3. Identifikation Operators

      • Hellmut Baumgärtel, Manfred Wollenberg
      Pages 195-232

    4. Structural Properties of Wave and Scattering Operators

      • Hellmut Baumgärtel, Manfred Wollenberg
      Pages 233-249

    5. Lax-Phillips Evolutions and Two-Space Wave Operators

      • Hellmut Baumgärtel, Manfred Wollenberg
      Pages 250-263

    6. Stationary Theory

      • Hellmut Baumgärtel, Manfred Wollenberg
      Pages 264-291

  6. Existence and Completeness of Wave Operators

    1. Front Matter

      Pages 299-300
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    2. Stationary methods

      • Hellmut Baumgärtel, Manfred Wollenberg
      Pages 301-321
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Keywords

About this book

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.

Authors and Affiliations

  • Institut für Mathematik, Akademie der Wissenschaften der DDR, Deutschland

    Hellmut Baumgärtel, Manfred Wollenberg

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