Spectral Properties of Hamiltonian Operators
Author : K. Jörgens
Publisher : Springer
Page : 144 pages
File Size : 36,85 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540383549
Author : K. Jörgens
Publisher : Springer
Page : 144 pages
File Size : 36,85 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540383549
Author : Werner Amrein
Publisher : Springer Science & Business Media
Page : 473 pages
File Size : 31,60 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 3034877625
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.
Author : K. Jorgens
Publisher :
Page : 152 pages
File Size : 36,59 MB
Release : 2014-01-15
Category :
ISBN : 9783662196144
Author : K. Jörgens
Publisher : Springer
Page : 146 pages
File Size : 12,33 MB
Release : 1973-04-20
Category : Mathematics
ISBN : 9783540061519
Author : M.A. Shubin
Publisher : Springer Science & Business Media
Page : 278 pages
File Size : 15,70 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 3662067196
This EMS volume contains a survey of the principles and advanced techniques of the spectral theory of linear differential and pseudodifferential operators in finite-dimensional spaces. Also including a special section of Sunada's recent solution of Kac's celebrated problem of whether or not "one can hear the shape of a drum".
Author : Klaus Bichteler
Publisher :
Page : 176 pages
File Size : 14,25 MB
Release : 1973
Category : Algebraic fields
ISBN : 9780387061511
Author : David Eric Edmunds
Publisher : Oxford University Press
Page : 610 pages
File Size : 26,94 MB
Release : 2018
Category : Mathematics
ISBN : 0198812051
This book is an updated version of the classic 1987 monograph "Spectral Theory and Differential Operators".The original book was a cutting edge account of the theory of bounded and closed linear operators in Banach and Hilbert spaces relevant to spectral problems involving differential equations. It is accessible to a graduate student as well as meeting the needs of seasoned researchers in mathematics and mathematical physics. This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.
Author : Rafael del Río
Publisher : American Mathematical Soc.
Page : 264 pages
File Size : 21,38 MB
Release : 2004
Category : Mathematics
ISBN : 0821832972
This volume gathers the articles based on a series of lectures from a workshop held at the Institute of Applied Mathematics of the National University of Mexico. The aim of the book is to present to a non-specialized audience the basic tools needed to understand and appreciate new trends of research on Schrodinger operator theory. Topics discussed include various aspects of the spectral theory of differential operators, the theory of self-adjoint operators, finite rank perturbations, spectral properties of random Schrodinger operators, and scattering theory for Schrodinger operators. The material is suitable for graduate students and research mathematicians interested in differential operators, in particular, spectral theory of Schrodinger operators.
Author : Werner O. Amrein
Publisher : Springer Science & Business Media
Page : 469 pages
File Size : 31,56 MB
Release : 2013-11-26
Category : Mathematics
ISBN : 3034807333
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)
Author : Carlos André
Publisher : Birkhäuser
Page : 381 pages
File Size : 11,19 MB
Release : 2018-08-22
Category : Mathematics
ISBN : 3319724495
This book consists of invited survey articles and research papers in the scientific areas of the “International Workshop on Operator Algebras, Operator Theory and Applications,” which was held in Lisbon in July 2016. Reflecting recent developments in the field of algebras of operators, operator theory and matrix theory, it particularly focuses on groupoid algebras and Fredholm conditions, algebras of approximation sequences, C* algebras of convolution type operators, index theorems, spectrum and numerical range of operators, extreme supercharacters of infinite groups, quantum dynamics and operator algebras, and inverse eigenvalue problems. Establishing bridges between the three related areas of operator algebras, operator theory, and matrix theory, the book is aimed at researchers and graduate students who use results from these areas.