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Author : Michael Stephen Patrick Eastham
Publisher : Unknown
Page : 148 pages
File Size : 48,5 Mb
Release : 1973
Category : Differential equations
ISBN : UOM:39015058965974
Author : M. S. Eastham
Publisher : Unknown
Page : 128 pages
File Size : 44,7 Mb
Release : 1974-07
Category : Electronic
ISBN : 0028441508
Author : Sebastian Klein
Publisher : Springer
Page : 326 pages
File Size : 48,6 Mb
Release : 2018-12-05
Category : Mathematics
ISBN : 9783030012762
This book develops a spectral theory for the integrable system of 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation. Such solutions (if real-valued) correspond to certain constant mean curvature surfaces in Euclidean 3-space. Spectral data for such solutions are defined (following ideas of Hitchin and Bobenko) and the space of spectral data is described by an asymptotic characterization. Using methods of asymptotic estimates, the inverse problem for the spectral data is solved along a line, i.e. the solution u is reconstructed on a line from the spectral data. Finally, a Jacobi variety and Abel map for the spectral curve are constructed and used to describe the change of the spectral data under translation of the solution u. The book's primary audience will be research mathematicians interested in the theory of infinite-dimensional integrable systems, or in the geometry of constant mean curvature surfaces.
Author : Fedor S. Rofe-Beketov,Aleksandr M. Khol'kin,Ognjen Milatovic
Publisher : World Scientific
Page : 466 pages
File Size : 53,9 Mb
Release : 2005
Category : Mathematics
ISBN : 9789812703453
This is the first monograph devoted to the Sturm oscillatory theory for infinite systems of differential equations and its relations with the spectral theory. It aims to study a theory of self-adjoint problems for such systems, based on an elegant method of binary relations. Another topic investigated in the book is the behavior of discrete eigenvalues which appear in spectral gaps of the Hill operator and almost periodic SchrAdinger operators due to local perturbations of the potential (e.g., modeling impurities in crystals). The book is based on results that have not been presented in other monographs. The only prerequisites needed to read it are basics of ordinary differential equations and operator theory. It should be accessible to graduate students, though its main topics are of interest to research mathematicians working in functional analysis, differential equations and mathematical physics, as well as to physicists interested in spectral theory of differential operators."
Author : B. Malcolm Brown,Michael S.P. Eastham,Karl Michael Schmidt
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 51,9 Mb
Release : 2012-10-30
Category : Mathematics
ISBN : 9783034805285
Periodic differential operators have a rich mathematical theory as well as important physical applications. They have been the subject of intensive development for over a century and remain a fertile research area. This book lays out the theoretical foundations and then moves on to give a coherent account of more recent results, relating in particular to the eigenvalue and spectral theory of the Hill and Dirac equations. The book will be valuable to advanced students and academics both for general reference and as an introduction to active research topics.
Author : Anonim
Publisher : Elsevier
Page : 209 pages
File Size : 55,5 Mb
Release : 2011-09-21
Category : Mathematics
ISBN : 0080871240
Spectral Theory and Asymptotics of Differential Equations
Author : Joachim Weidmann
Publisher : Lecture Notes in Mathematics
Page : 316 pages
File Size : 42,7 Mb
Release : 1987-05-06
Category : Mathematics
ISBN : STANFORD:36105032362860
These notes will be useful and of interest to mathematicians and physicists active in research as well as for students with some knowledge of the abstract theory of operators in Hilbert spaces. They give a complete spectral theory for ordinary differential expressions of arbitrary order n operating on -valued functions existence and construction of self-adjoint realizations via boundary conditions, determination and study of general properties of the resolvent, spectral representation and spectral resolution. Special attention is paid to the question of separated boundary conditions, spectral multiplicity and absolutely continuous spectrum. For the case nm=2 (Sturm-Liouville operators and Dirac systems) the classical theory of Weyl-Titchmarch is included. Oscillation theory for Sturm-Liouville operators and Dirac systems is developed and applied to the study of the essential and absolutely continuous spectrum. The results are illustrated by the explicit solution of a number of particular problems including the spectral theory one partical Schrödinger and Dirac operators with spherically symmetric potentials. The methods of proof are functionally analytic wherever possible.
Author : E. Khruslov,L. Pastur,D. Shepelsky
Publisher : American Mathematical Society
Page : 266 pages
File Size : 52,8 Mb
Release : 2014-09-26
Category : Mathematics
ISBN : 9781470416836
This volume is dedicated to V. A. Marchenko on the occasion of his 90th birthday. It contains refereed original papers and survey articles written by his colleagues and former students of international stature and focuses on the areas to which he made important contributions: spectral theory of differential and difference operators and related topics of mathematical physics, including inverse problems of spectral theory, homogenization theory, and the theory of integrable systems. The papers in the volume provide a comprehensive account of many of the most significant recent developments in that broad spectrum of areas.
Author : David Edmunds,Des Evans
Publisher : Oxford University Press
Page : 128 pages
File Size : 55,7 Mb
Release : 2018-05-03
Category : Mathematics
ISBN : 9780192540102
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 : W. N. Everitt
Publisher : Unknown
Page : 340 pages
File Size : 47,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 366217135X
Author : M. M. Skriganov
Publisher : American Mathematical Soc.
Page : 132 pages
File Size : 50,5 Mb
Release : 1987
Category : Mathematics
ISBN : 0821831046
Author : Michael Demuth,Bert-Wolfgang Schulze
Publisher : Birkhäuser
Page : 346 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882316
The intention of the international conference PDE2000 was to bring together specialists from different areas of modern analysis, mathematical physics and geometry, to discuss not only the recent progress in their own fields but also the interaction between these fields. The special topics of the conference were spectral and scattering theory, semiclassical and asymptotic analysis, pseudodifferential operators and their relation to geometry, as well as partial differential operators and their connection to stochastic analysis and to the theory of semigroups. The scientific advisory board of the conference in Clausthal consisted of M. Ben-Artzi (Jerusalem), Chen Hua (Peking), M. Demuth (Clausthal), T. Ichinose (Kanazawa), L. Rodino (Turin), B.-W. Schulze (Potsdam) and J. Sjöstrand (Paris). The book is aimed at researchers in mathematics and mathematical physics with interests in partial differential equations and all its related fields.
Author : Eduardus Marie de Jager
Publisher : Unknown
Page : 208 pages
File Size : 47,8 Mb
Release : 1974
Category : Electronic
ISBN : OCLC:251905240
Author : M.A. Shubin
Publisher : Springer Science & Business Media
Page : 278 pages
File Size : 53,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662067192
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 : W.N. Everitt
Publisher : Lecture Notes in Mathematics
Page : 340 pages
File Size : 54,7 Mb
Release : 1975-04-14
Category : Mathematics
ISBN : STANFORD:36105031599603
