Amrein, Werner O., Boutet de Monvel, Anne, Georgescu, Vladimir
Originally published as volume 135 in the series Progress in Mathematics
1996. Reprint 2013 of the 1996 edition, XIV, 460 p.
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Well-written research monograph that stimulates the further theory evolution of the field
Self-contained and accessible to advanced students
Provides auxiliary background material and develops the necessary tools from functional analysis
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.
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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)
Content Level »Research
Keywords »Mourre‘s commutator theory - algebraic framework for many-body problem - conjugate operator method - funtional analytic tools - many-channel Hamiltonians - spectral and scattering theory
Preface.- Comments on notations.- 1 Some Spaces of Functions and Distributions.- 2 Real Interpolation of Banach Spaces.- 3 C0-Groups and Functional Calculi.- 4 Some Examples of C0-Groups.- 5 Automorphisms Associated to C0-Representations.- 6 Unitary Representations and Regularity.- 7 The Conjugate Operator Method.- 8 An Algebraic Framework for the Many-Body Problem.- 9 Spectral Theory of N-Body Hamiltonians.- 10 Quantum-Mechanical N-Body Systems.- Bibliography.- Notations.- Index.