Share

Spectral Analysis Of Differential Operators: Interplay Between Spectral And Oscillatory Properties

2005-08-29 Mathematics
Download Spectral Analysis Of Differential Operators: Interplay Between Spectral And Oscillatory Properties PDF Online Free

Author :
Release : 2005-08-29
Genre : Mathematics
Kind : eBook
Book Rating : 673/5 ( reviews)

GET EBOOK


Book Synopsis Spectral Analysis Of Differential Operators: Interplay Between Spectral And Oscillatory Properties by : Fedor S Rofe-beketov

Download or read book Spectral Analysis Of Differential Operators: Interplay Between Spectral And Oscillatory Properties written by Fedor S Rofe-beketov. This book was released on 2005-08-29. 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 Schrödinger 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.

A Guide to Spectral Theory

2021-05-06 Mathematics
Download A Guide to Spectral Theory PDF Online Free

Author :
Release : 2021-05-06
Genre : Mathematics
Kind : eBook
Book Rating : 622/5 ( reviews)

GET EBOOK


Book Synopsis A Guide to Spectral Theory by : Christophe Cheverry

Download or read book A Guide to Spectral Theory written by Christophe Cheverry. This book was released on 2021-05-06. 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.

Recent Developments in the Solution of Nonlinear Differential Equations

2021-09-08 Mathematics
Download Recent Developments in the Solution of Nonlinear Differential Equations PDF Online Free

Author :
Release : 2021-09-08
Genre : Mathematics
Kind : eBook
Book Rating : 561/5 ( reviews)

GET EBOOK


Book Synopsis Recent Developments in the Solution of Nonlinear Differential Equations by : Bruno Carpentieri

Download or read book Recent Developments in the Solution of Nonlinear Differential Equations written by Bruno Carpentieri. This book was released on 2021-09-08. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear differential equations are ubiquitous in computational science and engineering modeling, fluid dynamics, finance, and quantum mechanics, among other areas. Nowadays, solving challenging problems in an industrial setting requires a continuous interplay between the theory of such systems and the development and use of sophisticated computational methods that can guide and support the theoretical findings via practical computer simulations. Owing to the impressive development in computer technology and the introduction of fast numerical methods with reduced algorithmic and memory complexity, rigorous solutions in many applications have become possible. This book collects research papers from leading world experts in the field, highlighting ongoing trends, progress, and open problems in this critically important area of mathematics.

Ordinary Differential Operators

2019-11-08 Education
Download Ordinary Differential Operators PDF Online Free

Author :
Release : 2019-11-08
Genre : Education
Kind : eBook
Book Rating : 665/5 ( reviews)

GET EBOOK


Book Synopsis Ordinary Differential Operators by : Aiping Wang

Download or read book Ordinary Differential Operators written by Aiping Wang. This book was released on 2019-11-08. Available in PDF, EPUB and Kindle. Book excerpt: In 1910 Herman Weyl published one of the most widely quoted papers of the 20th century in Analysis, which initiated the study of singular Sturm-Liouville problems. The work on the foundations of Quantum Mechanics in the 1920s and 1930s, including the proof of the spectral theorem for unbounded self-adjoint operators in Hilbert space by von Neumann and Stone, provided some of the motivation for the study of differential operators in Hilbert space with particular emphasis on self-adjoint operators and their spectrum. Since then the topic developed in several directions and many results and applications have been obtained. In this monograph the authors summarize some of these directions discussing self-adjoint, symmetric, and dissipative operators in Hilbert and Symplectic Geometry spaces. Part I of the book covers the theory of differential and quasi-differential expressions and equations, existence and uniqueness of solutions, continuous and differentiable dependence on initial data, adjoint expressions, the Lagrange Identity, minimal and maximal operators, etc. In Part II characterizations of the symmetric, self-adjoint, and dissipative boundary conditions are established. In particular, the authors prove the long standing Deficiency Index Conjecture. In Part III the symmetric and self-adjoint characterizations are extended to two-interval problems. These problems have solutions which have jump discontinuities in the interior of the underlying interval. These jumps may be infinite at singular interior points. Part IV is devoted to the construction of the regular Green's function. The construction presented differs from the usual one as found, for example, in the classical book by Coddington and Levinson.

Topics in Operator Theory

2011-02-03 Mathematics
Download Topics in Operator Theory PDF Online Free

Author :
Release : 2011-02-03
Genre : Mathematics
Kind : eBook
Book Rating : 611/5 ( reviews)

GET EBOOK


Book Synopsis Topics in Operator Theory by : Joseph A. Ball

Download or read book Topics in Operator Theory written by Joseph A. Ball. This book was released on 2011-02-03. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.

You may also like...