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Mathematical Scattering Theory: General Theory
D. R. Yafaev, Université Rennes 1, France
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Translations of Mathematical Monographs
1992; 341 pp; softcover
Volume: 105
Reprint/Revision History:
reprinted with corrections 1998
ISBN-10: 0-8218-0951-2
ISBN-13: 978-0-8218-0951-8
List Price: US$114
Member Price: US$91.20
Order Code: MMONO/105.S
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Scattering theory presents an excellent example of interaction between different mathematical subjects: operator theory, measure theory, the theory of differential operators and equations, mathematical analysis, and applications of these areas to quantum mechanics. Because of the interplay of these fields, a deep understanding of scattering theory can lead to deep insights into the developing world of modern mathematics.

Yafaev's book provides such an understanding of scattering theory, starting with basic principles and extending to current research. He presents a comprehensive and systematic exposition of the theory, covering different methods (of trace class and smooth perturbations) and approaches (time dependent and stationary) and discussing the relationships among them. Yafaev also fills some gaps in the monographic literature, such as the properties of the scattering matrix and the theory of the spectral shift function. The theory is developed for operators in abstract Hilbert space but is oriented to concrete applications to differential operators (of Schrödinger type). Addressed to graduate students as well as researchers, this book will prove an invaluable reference and research tool.

Readership

Graduate students as well as experts in theoretical and mathematical physics, differential and integral equations and mathematical analysis.

Reviews

"A book one can learn from."

-- The Bulletin of Mathematics Books

"Fills a gap in the literature ... explanations and descriptions are clear and understandable for readers who are familiar with the framework and fundamentals of the scattering theory ... provides a complete view of the time-independent theory excluding the resonance theory."

-- Zentralblatt MATH

"The volume is well organized and is a fine guide for a serious reader and a good source of information to research workers in the field."

-- Bulletin of the AMS

Table of Contents

  • Preliminary facts
  • Basic concepts of scattering theory
  • Further properties of the WO
  • Scattering for relatively smooth perturbations
  • The general setup in stationary scattering theory
  • Scattering for perturbations of trace class type
  • Properties of the scattering matrix (SM)
  • The spectral shift function (SSF) and the trace formula
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