Some Problems In Nonlinear Spectral Theory
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Nonlinear Spectral Theory
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Author : Jürgen Appell
language : en
Publisher: Walter de Gruyter
Release Date : 2004
Nonlinear Spectral Theory written by Jürgen Appell and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
In view of the eminent importance of spectral theory of linear operators in many fields of mathematics and physics, it is not surprising that various attempts have been made to define and study spectra also for nonlinear operators. This book provides a comprehensive and self-contained treatment of the theory, methods, and applications of nonlinear spectral theory. The first chapter briefly recalls the definition and properties of the spectrum and several subspectra for bounded linear operators. Then some numerical characteristics for nonlinear operators are introduced which are useful for describing those classes of operators for which there exists a spectral theory. Since spectral values are closely related to solvability results for operator equations, various conditions for the local or global invertibility of a nonlinear operator are collected in the third chapter. The following two chapters are concerned with spectra for certain classes of continuous, Lipschitz continuous, or differentiable operators. These spectra, however, simply adapt the corresponding definitions from the linear theory which somehow restricts their applicability. Other spectra which are defined in a completely different way, but seem to have useful applications, are defined and studied in the following four chapters. The remaining three chapters are more application-oriented and deal with nonlinear eigenvalue problems, numerical ranges, and selected applications to nonlinear problems. The only prerequisite for understanding this book is a modest background in functional analysis and operator theory. It is addressed to non-specialists who want to get an idea of the development of spectral theory for nonlinear operators in the last 30 years, as well as a glimpse of the diversity of the directions in which current research is moving.
Some Problems In Nonlinear Spectral Theory
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Author : R. Chiappinelli
language : en
Publisher:
Release Date : 1986
Some Problems In Nonlinear Spectral Theory written by R. Chiappinelli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
Nonlinear Spectral Theory
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Author : Jürgen Appell
language : en
Publisher: Walter de Gruyter
Release Date : 2008-08-22
Nonlinear Spectral Theory written by Jürgen Appell and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-22 with Mathematics categories.
In view of the eminent importance of spectral theory of linear operators in many fields of mathematics and physics, it is not surprising that various attempts have been made to define and study spectra also for nonlinear operators. This book provides a comprehensive and self-contained treatment of the theory, methods, and applications of nonlinear spectral theory. The first chapter briefly recalls the definition and properties of the spectrum and several subspectra for bounded linear operators. Then some numerical characteristics for nonlinear operators are introduced which are useful for describing those classes of operators for which there exists a spectral theory. Since spectral values are closely related to solvability results for operator equations, various conditions for the local or global invertibility of a nonlinear operator are collected in the third chapter. The following two chapters are concerned with spectra for certain classes of continuous, Lipschitz continuous, or differentiable operators. These spectra, however, simply adapt the corresponding definitions from the linear theory which somehow restricts their applicability. Other spectra which are defined in a completely different way, but seem to have useful applications, are defined and studied in the following four chapters. The remaining three chapters are more application-oriented and deal with nonlinear eigenvalue problems, numerical ranges, and selected applications to nonlinear problems. The only prerequisite for understanding this book is a modest background in functional analysis and operator theory. It is addressed to non-specialists who want to get an idea of the development of spectral theory for nonlinear operators in the last 30 years, as well as a glimpse of the diversity of the directions in which current research is moving.
Introduction To The Spectral Theory Of Polynomial Operator Pencils
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Author : A. S. Markus
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-09-14
Introduction To The Spectral Theory Of Polynomial Operator Pencils written by A. S. Markus and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-14 with Education categories.
This monograph contains an exposition of the foundations of the spectral theory of polynomial operator pencils acting in a Hilbert space. Spectral problems for polynomial pencils have attracted a steady interest in the last 35 years, mainly because they arise naturally in such diverse areas of mathematical physics as differential equations and boundary value problems, controllable systems, the theory of oscillations and waves, elasticity theory, and hydromechanics. In this book, the author devotes most of his attention to the fundamental results of Keldysh on multiple completeness of the eigenvectors and associate vectors of a pencil, and on the asymptotic behavior of its eigenvalues and generalizations of these results. The author also presents various theorems on spectral factorization of pencils which grew out of known results of M. G. Krein and Heinz Langer. A large portion of the book involves the theory of selfadjoint pencils, an area having numerous applications. Intended for mathematicians, researchers in mechanics, and theoretical physicists interested in spectral theory and its applications, the book assumes a familiarity with the fundamentals of spectral theory of operators acting in a Hilbert space.
Jacobi Matrices And The Moment Problem
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Author : Yurij M. Berezansky
language : en
Publisher: Springer Nature
Release Date : 2023-11-29
Jacobi Matrices And The Moment Problem written by Yurij M. Berezansky and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-29 with Mathematics categories.
This monograph presents the solution of the classical moment problem, the construction of Jacobi matrices and corresponding polynomials. The cases of strongly,trigonometric, complex and real two-dimensional moment problems are discussed, and the Jacobi-type matrices corresponding to the trigonometric moment problem are shown. The Berezansky theory of the expansion in generalized eigenvectors for corresponding set of commuting operators plays the key role in the proof of results. The book is recommended for researchers in fields of functional analysis, operator theory, mathematical physics, and engineers who deal with problems of coupled pendulums.
Inverse Problems And Nonlinear Evolution Equations
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Author : Alexander L. Sakhnovich
language : en
Publisher: Walter de Gruyter
Release Date : 2013-07-31
Inverse Problems And Nonlinear Evolution Equations written by Alexander L. Sakhnovich and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-31 with Mathematics categories.
This book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich. The notion of the transfer matrix function generated by the S-node plays an essential role. The authors present fundamental solutions of various important systems of differential equations using the transfer matrix function, that is, either directly in the form of the transfer matrix function or via the representation in this form of the corresponding Darboux matrix, when Bäcklund–Darboux transformations and explicit solutions are considered. The transfer matrix function representation of the fundamental solution yields solution of an inverse problem, namely, the problem to recover system from its Weyl function. Weyl theories of selfadjoint and skew-selfadjoint Dirac systems, related canonical systems, discrete Dirac systems, system auxiliary to the N-wave equation and a system rationally depending on the spectral parameter are obtained in this way. The results on direct and inverse problems are applied in turn to the study of the initial-boundary value problems for integrable (nonlinear) wave equations via inverse spectral transformation method. Evolution of the Weyl function and solution of the initial-boundary value problem in a semi-strip are derived for many important nonlinear equations. Some uniqueness and global existence results are also proved in detail using evolution formulas. The reading of the book requires only some basic knowledge of linear algebra, calculus and operator theory from the standard university courses.
30 Years Review Of China S Science And Technology 1949 1979
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Author :
language : en
Publisher: World Scientific
Release Date : 1982-01-01
30 Years Review Of China S Science And Technology 1949 1979 written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-01-01 with Science categories.
This is the 1st China's Science Yearbook published since 1949. It covers events, activities and progresses in various fields of science and technology from 1949 to 1979. Published in conjunction with Shanghai Scientific Publishing Co., it was compiled and edited by a research team from 'Nature Magazine', Shanghai, People's Republic of China.
Theory Of Nonlinear Operators
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Author : J. Nečas
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 1974-12-31
Theory Of Nonlinear Operators written by J. Nečas and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-12-31 with Mathematics categories.
No detailed description available for "Theory of Nonlinear Operators".
Grants And Awards For The Fiscal Year Ended
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Author : National Science Foundation (U.S.)
language : en
Publisher:
Release Date : 1981
Grants And Awards For The Fiscal Year Ended written by National Science Foundation (U.S.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Federal aid to research categories.
Methods And Applications Of Statistics In Business Finance And Management Science
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Author : Narayanaswamy Balakrishnan
language : en
Publisher: John Wiley & Sons
Release Date : 2010-07-13
Methods And Applications Of Statistics In Business Finance And Management Science written by Narayanaswamy Balakrishnan and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-13 with Mathematics categories.
Inspired by the Encyclopedia of Statistical Sciences, Second Edition, this volume presents the tools and techniques that are essential for carrying out best practices in the modern business world The collection and analysis of quantitative data drives some of the most important conclusions that are drawn in today's business world, such as the preferences of a customer base, the quality of manufactured products, the marketing of products, and the availability of financial resources. As a result, it is essential for individuals working in this environment to have the knowledge and skills to interpret and use statistical techniques in various scenarios. Addressing this need, Methods and Applications of Statistics in Business, Finance, and Management Science serves as a single, one-of-a-kind resource that guides readers through the use of common statistical practices by presenting real-world applications from the fields of business, economics, finance, operations research, and management science. Uniting established literature with the latest research, this volume features classic articles from the acclaimed Encyclopedia of Statistical Sciences, Second Edition along with brand-new contributions written by today's leading academics and practitioners. The result is a compilation that explores classic methodology and new topics, including: Analytical methods for risk management Statistical modeling for online auctions Ranking and selection in mutual funds Uses of Black-Scholes formula in finance Data mining in prediction markets From auditing and marketing to stock market price indices and banking, the presented literature sheds light on the use of quantitative methods in research relating to common financial applications. In addition, the book supplies insight on common uses of statistical techniques such as Bayesian methods, optimization, simulation, forecasting, mathematical modeling, financial time series, and data mining in modern research. Providing a blend of traditional methodology and the latest research, Methods and Applications of Statistics in Business, Finance, and Management Science is an excellent reference for researchers, managers, consultants, and students in the fields of business, management science, operations research, supply chain management, mathematical finance, and economics who must understand statistical literature and carry out quantitative practices to make smart business decisions in their everyday work.