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A Spectral Theory For Simply Periodic Solutions Of The Sinh Gordon Equation
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Book Synopsis A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation by : Sebastian Klein
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.
Book Synopsis Spectral Theory and Differential Equations by : E. Khruslov
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.
Book Synopsis Spectral Theory for Bounded Functions and Applications to Evolution Equations by : Gaston M. N'Guerekata
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.
Book Synopsis Spectral Theory and Asymptotics of Differential Equations by :
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 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral Theory and Asymptotics of Differential Equations
Book Synopsis Spectral Theory and Differential Equations by : W. N. Everitt
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:
Book Synopsis Spectral Theory and Differential Equations by : W.N. Everitt
Download or read book Spectral Theory and Differential Equations written by W.N. Everitt and published by Springer. This book was released on 2006-11-15 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to spectral theory: selfadjoint ordinary differential operators by : Boris Moiseevich Levitan
Download or read book Introduction to spectral theory: selfadjoint ordinary differential operators written by Boris Moiseevich Levitan and published by American Mathematical Soc.. This book was released on 1975 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a monograph that is devoted to the spectral theory of the Sturm- Liouville operator and to the spectral theory of the Dirac system. This book concerns with nth order operators that can serve as simply an introduction to this domain. It includes a chapter that discusses this theory.
Book Synopsis Spectral Theory and asymptotics of differential equations by : Eduardus Marie de Jager
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:
Book Synopsis Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications by : Janusz Mierczynski
Download or read book Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications written by Janusz Mierczynski and published by Chapman and Hall/CRC. This book was released on 2008-03-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a basic tool for studying nonlinear problems, Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications focuses on the principal spectral theory for general time-dependent and random parabolic equations and systems. The text contains many new results and considers existing results from a fresh perspective. Taking a clear, unified, and self-contained approach, the authors first develop the abstract general theory in the framework of weak solutions, before turning to cases of random and nonautonomous equations. They prove that time dependence and randomness do not reduce the principal spectrum and Lyapunov exponents of nonautonomous and random parabolic equations. The book also addresses classical Faber–Krahn inequalities for elliptic and time-periodic problems and extends the linear theory for scalar nonautonomous and random parabolic equations to cooperative systems. The final chapter presents applications to Kolmogorov systems of parabolic equations. By thoroughly explaining the spectral theory for nonautonomous and random linear parabolic equations, this resource reveals the importance of the theory in examining nonlinear problems.
Book Synopsis Spectral Theory for Bounded Functions and Applications to Evolution Equations by : Gaston M. N'Guerekata
Download or read book Spectral Theory for Bounded Functions and Applications to Evolution Equations written by Gaston M. N'Guerekata and published by . This book was released on 2017 with total page 0 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 generalisations, 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. Its our hope that this first monograph ever on this topic will attract more researchers.
Book Synopsis Spectral Theory and Wave Processes by : M. Sh. Birman
Download or read book Spectral Theory and Wave Processes written by M. Sh. Birman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this collection are devoted to various problems in mathematical physics and mathematical analysis, primarily in the fields of spectral theory and the theory of wave processes. The collection is intended for mathematicians sPf>cializing in the fields of mathematical physics, functional analysis, and the theory of differential equations. In addition, it is of some interest to theoretical physicists. The first paper deals with a mixed boundary value problem for a system of elasticity equations, and considers fields in the neighborhood of various wave fronts. The method used permits an estimate of the errors in the Ben-Menahem approximate method. Paper 2 investigates operators in separable Hilbert space given by double integrals of a type defined at the beginning of the paper, and in which integration is understood as the limit of the integral sums of Riemann-stieltjes. In paper 3, the problem of calculation of elastic constants for a laminarly inhomogeneous semi-infinite medium is conSidered, and the uniqueness of the solution of the inverse seismic problem at finite depth proved. The fourth paper gives a detailed account of the results of an earlier paper by the same author, in which he generalized to the three-dimensional case the trace formulas obtained for the one-dimensional Schroedinger operator. Asymptotic estimates of the resolvent kernel and solutions of the scattering problem are given.
Book Synopsis Spectral Theory and Asymptotic Behavior of Linear Almost Periodic Differential Equations by :
Download or read book Spectral Theory and Asymptotic Behavior of Linear Almost Periodic Differential Equations written by and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book 数理科学講究錄 written by and published by . This book was released on 1978 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Spectral Theory and Asymptotic Behavior of Linear Almost Periodic Differential Equations by : Xuan Dieu Bui
Download or read book Spectral Theory and Asymptotic Behavior of Linear Almost Periodic Differential Equations written by Xuan Dieu Bui and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Spectral Theory and Asymptotics of Differential Equations by :
Download or read book Spectral Theory and Asymptotics of Differential Equations written by and published by . This book was released on 1974 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Guide to Spectral Theory by : Christophe Cheverry
Download or read book A Guide to Spectral Theory written by Christophe Cheverry and published by Birkhäuser. This book was released on 2022-05-07 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a graduate-level introduction to the spectral theory of linear operators on Banach and Hilbert spaces, guiding readers through key components of spectral theory and its applications in quantum physics. Based on their extensive teaching experience, the authors present topics in a progressive manner so that each chapter builds on the ones preceding. Researchers and students alike will also appreciate the exploration of more advanced applications and research perspectives presented near the end of the book. Beginning with a brief introduction to the relationship between spectral theory and quantum physics, the authors go on to explore unbounded operators, analyzing closed, adjoint, and self-adjoint operators. Next, the spectrum of a closed operator is defined and the fundamental properties of Fredholm operators are introduced. The authors then develop the Grushin method to execute the spectral analysis of compact operators. The chapters that follow are devoted to examining Hille-Yoshida and Stone theorems, the spectral analysis of self-adjoint operators, and trace-class and Hilbert-Schmidt operators. The final chapter opens the discussion to several selected applications. Throughout this textbook, detailed proofs are given, and the statements are illustrated by a number of well-chosen examples. At the end, an appendix about foundational functional analysis theorems is provided to help the uninitiated reader. A Guide to Spectral Theory: Applications and Exercises is intended for graduate students taking an introductory course in spectral theory or operator theory. A background in linear functional analysis and partial differential equations is assumed; basic knowledge of bounded linear operators is useful but not required. PhD students and researchers will also find this volume to be of interest, particularly the research directions provided in later chapters.
Download or read book Spectral Theory written by M. Sh Birman and published by . This book was released on 1969 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:
