C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians

1. Front Matter

   Pages i-xiv

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2. Some Spaces of Functions and Distributions

   • Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu

   Pages 1-28

3. Real Interpolation of Banach Spaces

   • Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu

   Pages 29-72

4. C0-Groups and Functional Calculi

   • Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu

   Pages 73-170

5. Some Examples of C0-Groups

   • Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu

   Pages 171-190

6. Groups of Automorphisms Associated to C ₀-Representations of ℝⁿ

   • Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu

   Pages 191-233

7. Unitary Representations and Regularity for Self-Adjoint Operators

   • Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu

   Pages 235-265

8. The Conjugate Operator Method

   • Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu

   Pages 267-356

9. An Algebraic Framework for the Many-Body Problem

   • Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu

   Pages 357-399

10. Spectral Theory of N-Body Hamiltonians

    • Werner O. Amrein, Anne Boutet de Monvel, V. Georgescu

    Pages 401-432

11. Quantum–Mechanical N-Body Systems

    • Werner O Amrein, Anne Boutet de Monvel, Vladimir Georgescu

    Pages 433-443

12. Back Matter

    Pages 445-460

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The conjugate operator method is a powerful recently developed technique for studying spectral properties of self-adjoint operators. One of the purposes of this volume is to present a refinement of the original method due to Mourre leading to essentially optimal results in situations as varied as ordinary differential operators, pseudo-differential operators and N-body Schrödinger hamiltonians. Another topic is a new algebraic framework for the N-body problem allowing a simple and systematic treatment of large classes of many-channel hamiltonians. The monograph will be of interest to research mathematicians and mathematical physicists. The authors have made efforts to produce an essentially self-contained text, which makes it accessible to advanced students. Thus about one third of the book is devoted to the development of tools from functional analysis, in particular real interpolation theory for Banach spaces and functional calculus and Besov spaces associated with multi-parameter C0-groups. Certainly this monograph (containing a bibliography of 170 items) is a well-written contribution to this field which is suitable to stimulate further evolution of the theory. (Mathematical Reviews)

• Mourre‘s commutator theory
• algebraic framework for many-body problem
• conjugate operator method
• funtional analytic tools
• many-channel Hamiltonians
• spectral and scattering theory
• algebra
• automorphism
• differential operator
• distribution
• functional analysis
• Interpolation
• spectral theory

• Ecole de Physique, Université de Genève, Genève, Switzerland

  Werner O. Amrein

• Institut de Mathématiques de Jussieu, Université Paris Diderot, Paris, France

  Anne Boutet de Monvel

• Département de Mathématiques, Université de Cergy-Pontoise, Cergy-Pontoise, France

  Vladimir Georgescu

Werner O. Amrein is a Professor of Mathematics at the University of Geneva, Switzerland.
Anne Boutet de Monvel is a Professor of Mathematics at the University Paris Diderot, France.
Vladimir Georgescu is a Professor of Mathematics at the University of Cergy-Pontoise, France.

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