The conjugate operator method is a powerful recently develop- ed 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 algeb- raic framework for the N-body problem allowing a simple and systematic treatment of large classes of many-channel hamil- tonians. 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.
Author(s): Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu (auth.)
Series: Progress in Mathematics 135
Publisher: Birkhäuser Basel
Year: 1996
Language: English
Pages: 480
Tags: Analysis; Theoretical, Mathematical and Computational Physics
Front Matter....Pages i-xiv
Some Spaces of Functions and Distributions....Pages 1-28
Real Interpolation of Banach Spaces....Pages 29-72
C 0 -Groups and Functional Calculi....Pages 73-170
Some Examples of C 0 -Groups....Pages 171-190
Groups of Automorphisms Associated to C 0 -Representations of ℝ n ....Pages 191-233
Unitary Representations and Regularity for Self-adjoint Operators....Pages 235-265
The Conjugate Operator Method....Pages 267-356
An Algebraic Framework for the Many-Body Problem....Pages 357-399
Spectral Theory of N -Body Hamiltonians....Pages 401-432
Quantum-Mechanical N -Body Systems....Pages 433-443
Back Matter....Pages 445-464