Overview
- Authors:
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Werner O. Amrein
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Ecole de Physique, Université de Genève, Genève 4, Switzerland
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Anne Boutet Monvel
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Institut de Mathématiques de Paris-Jussieu, C.N.R.S. UMR 9994, Université Paris VII Denis Diderot, Paris Cedex 05, France
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Vladimir Georgescu
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Institut de Mathématiques de Paris-Jussieu, C.N.R.S. UMR 9994, Université Paris VII Denis Diderot, Paris Cedex 05, France
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Table of contents (10 chapters)
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- Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
Pages 1-28
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- Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
Pages 29-72
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- Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
Pages 73-170
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- Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
Pages 171-190
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- Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
Pages 191-233
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- Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
Pages 235-265
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- Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
Pages 267-356
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- Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
Pages 357-399
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- Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
Pages 401-432
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- Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu
Pages 433-443
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Back Matter
Pages 445-464
About this book
The relevance of commutator methods in spectral and scattering theory has been known for a long time, and numerous interesting results have been ob tained by such methods. The reader may find a description and references in the books by Putnam [Pu], Reed-Simon [RS] and Baumgartel-Wollenberg [BW] for example. A new point of view emerged around 1979 with the work of E. Mourre in which the method of locally conjugate operators was introduced. His idea proved to be remarkably fruitful in establishing detailed spectral properties of N-body Hamiltonians. A problem that was considered extremely difficult be fore that time, the proof of the absence of a singularly continuous spectrum for such operators, was then solved in a rather straightforward manner (by E. Mourre himself for N = 3 and by P. Perry, 1. Sigal and B. Simon for general N). The Mourre estimate, which is the main input of the method, also has consequences concerning the behaviour of N-body systems at large times. A deeper study of such propagation properties allowed 1. Sigal and A. Soffer in 1985 to prove existence and completeness of wave operators for N-body systems with short range interactions without implicit conditions on the potentials (for N = 3, similar results were obtained before by means of purely time-dependent methods by V. Enss and by K. Sinha, M. Krishna and P. Muthuramalingam). Our interest in commutator methods was raised by the major achievements mentioned above.
