Download or read book The Spectral Theory of Periodic Differential Equations written by Michael Stephen Patrick Eastham and published by . This book was released on 1973 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Theory of Periodic Differential Equations written by M. S. Eastham and published by . This book was released on 1974-07 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Spectral Theory for Simply Periodic Solutions of the Sinh Gordon Equation written by Sebastian Klein and published by Springer. This book was released on 2018-12-05 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spectral Analysis of Differential Operators written by Fedor S. Rofe-Beketov and published by World Scientific. This book was released on 2005 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."
Download or read book Spectral Theory and Asymptotics of Differential Equations written by and published by Elsevier. This book was released on 2011-09-21 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral Theory and Asymptotics of Differential Equations
Download or read book Periodic Differential Operators written by B. Malcolm Brown and published by Springer Science & Business Media. This book was released on 2012-10-30 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spectral Theory of Ordinary Differential Operators written by Joachim Weidmann and published by Lecture Notes in Mathematics. This book was released on 1987-05-06 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spectral Theory and Differential Equations written by E. Khruslov and published by American Mathematical Society. This book was released on 2014-09-26 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spectral Theory and Differential Equations written by W. N. Everitt and published by . This book was released on 2014-01-15 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Theory and Differential Operators written by David Edmunds and published by Oxford University Press. This book was released on 2018-05-03 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Partial Differential Equations VII written by M.A. Shubin and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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".
Download or read book Partial Differential Equations written by and published by . This book was released on 1991 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric and Arithmetic Methods in the Spectral Theory of Multidimensional Periodic Operators written by M. M. Skriganov and published by American Mathematical Soc.. This book was released on 1987 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Theory for Bounded Functions and Applications to Evolution Equations written by Gaston M. N'Guerekata and published by Nova Science Publishers. This book was released on 2017 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the central questions in the qualitative theory of difference and differential equations is to find the conditions of existence and asymptotic behavior of bounded solutions. For equations with almost periodic coefficients, the problem concerns Favard and Perron. A remarkable theory has been developed in harmonic analysis with outstanding contributions by Loomis, Arendt, Batty, Lyubic, Phong, Naito, Minh and many others, when the Carleman spectrum of the functions is countable. Uniform continuity in this case plays a key role. In the absence of this condition, the theory does not apply. This led to the introduction over the last decade of new types of spectrum functions which helped solve the problem, especially in the case of almost automorphic functions by using the theory of commutating operators.This monograph presents a unique and unified manner of recent developments in the theory of bounded continuous functions, including the space of (Bohr) almost periodic functions and some of their generalizations, and the spaces of (Bochner) almost automorphic functions and almost automorphic sequences. Classical concepts from harmonic analysis such as the Bohr spectrum, Beurling spectrum and Carleman spectrum are also presented with some examples. Special attention is devoted to the recently introduced concepts of uniform spectrum and circular spectrum of bounded functions derived from the study of linear differential equation solutions, whose forcing terms are not necessarily uniformly continuous. Connections between these various types of spectra are also investigated. The book provides a semigroup-free study of the existence and asymptotic behavior of mild solutions concerning evolution equations of the first and second order as well as difference equations. Bibliographical and historical notes complete the major chapters. An appendix reviewing basic results on the theory of commutating operators is given. The content is presented in a way that is easily accessible to readers who are working in differential equations, but are not familiar with harmonic analysis and advanced functional analysis. It's our hope that this first monograph ever on this topic will attract more researchers.
Download or read book Partial Differential Equations and Spectral Theory written by Michael Demuth and published by Birkhäuser. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spectral Theory and Differential Equations written by W.N. Everitt and published by Lecture Notes in Mathematics. This book was released on 1975-04-14 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Theory and asymptotics of differential equations written by Eduardus Marie de Jager and published by . This book was released on 1974 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
