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Author: Rubén Figueroa Sestelo
Publisher: Springer Nature
ISBN: 3030816044
Category : Mathematics
Languages : en
Pages : 194
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Book Description
This unique book contains a generalization of the Leray-Schauder degree theory which applies for wide and meaningful types of discontinuous operators. The discontinuous degree theory introduced in the first section is subsequently used to prove new, applicable, discontinuous versions of many classical fixed-point theorems such as Schauder’s. Finally, readers will find in this book several applications of those discontinuous fixed-point theorems in the proofs of new existence results for discontinuous differential problems. Written in a clear, expository style, with the inclusion of many examples in each chapter, this book aims to be useful not only as a self-contained reference for mature researchers in nonlinear analysis but also for graduate students looking for a quick accessible introduction to degree theory techniques for discontinuous differential equations.
Author: Rubén Figueroa Sestelo
Publisher: Springer Nature
ISBN: 3030816044
Category : Mathematics
Languages : en
Pages : 194
Get Book Here
Book Description
This unique book contains a generalization of the Leray-Schauder degree theory which applies for wide and meaningful types of discontinuous operators. The discontinuous degree theory introduced in the first section is subsequently used to prove new, applicable, discontinuous versions of many classical fixed-point theorems such as Schauder’s. Finally, readers will find in this book several applications of those discontinuous fixed-point theorems in the proofs of new existence results for discontinuous differential problems. Written in a clear, expository style, with the inclusion of many examples in each chapter, this book aims to be useful not only as a self-contained reference for mature researchers in nonlinear analysis but also for graduate students looking for a quick accessible introduction to degree theory techniques for discontinuous differential equations.
Author: Athanass Kartsatos
Publisher: CRC Press
ISBN: 9780824797218
Category : Mathematics
Languages : en
Pages : 338
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Book Description
This work is based upon a Special Session on the Theory and Applications of Nonlinear Operators of Accretive and Monotone Type held during the recent meeting of the American Mathematical Society in San Francisco. It examines current developments in non-linear analysis, emphasizing accretive and monotone operator theory. The book presents a major survey/research article on partial functional differential equations with delay and an important survey/research article on approximation solvability.
Author: Rubén Figueroa Sestelo
Publisher: Springer
ISBN: 9783030816063
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This unique book contains a generalization of the Leray-Schauder degree theory which applies for wide and meaningful types of discontinuous operators. The discontinuous degree theory introduced in the first section is subsequently used to prove new, applicable, discontinuous versions of many classical fixed-point theorems such as Schauder’s. Finally, readers will find in this book several applications of those discontinuous fixed-point theorems in the proofs of new existence results for discontinuous differential problems. Written in a clear, expository style, with the inclusion of many examples in each chapter, this book aims to be useful not only as a self-contained reference for mature researchers in nonlinear analysis but also for graduate students looking for a quick accessible introduction to degree theory techniques for discontinuous differential equations.
Author:
Publisher: ScholarlyEditions
ISBN: 1464965315
Category : Mathematics
Languages : en
Pages : 743
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Book Description
Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Calculus, Mathematical Analysis, and Nonlinear Research. The editors have built Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Calculus, Mathematical Analysis, and Nonlinear Research in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Author: John B. Conway
Publisher: American Mathematical Soc.
ISBN: 0821815369
Category : Mathematics
Languages : en
Pages : 454
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Book Description
"In a certain sense, subnormal operators were introduced too soon because the theory of function algebras and rational approximation was also in its infancy and could not be properly used to examine the class of operators. The progress in the last several years grew out of applying the results of rational approximation." from the Preface. This book is the successor to the author's 1981 book on the same subject. In addition to reflecting the great strides in the development of subnormal operator theory since the first book, the present work is oriented towards rational functions rather than polynomials. Although the book is a research monograph, it has many of the traits of a textbook including exercises. The book requires background in function theory and functional analysis, but is otherwise fairly self-contained. The first few chapters cover the basics about subnormal operator theory and present a study of analytic functions on the unit disk. Other topics included are: some results on hypernormal operators, an exposition of rational approximation interspersed with applications to operator theory, a study of weak-star rational approximation, a set of results that can be termed structure theorems for subnormal operators, and a proof that analytic bounded point evaluations exist.
Author: Mark Aleksandrovich Krasnoselʹskiĭ
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 440
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Book Description
Geometrical (in particular, topological) methods in nonlinear analysis were originally invented by Banach, Birkhoff, Kellogg, Schauder, Leray, and others in existence proofs. Since about the fifties, these methods turned out to be essentially the sole approach to a variety of new problems: the investigation of iteration processes and other procedures in numerical analysis, in bifur cation problems and branching of solutions, estimates on the number of solutions and criteria for the existence of nonzero solutions, the analysis of the structure of the solution set, etc. These methods have been widely applied to the theory of forced vibrations and auto-oscillations, to various problems in the theory of elasticity and fluid. mechanics, to control theory, theoretical physics, and various parts of mathematics. At present, nonlinear analysis along with its geometrical, topological, analytical, variational, and other methods is developing tremendously thanks to research work in many countries. Totally new ideas have been advanced, difficult problems have been solved, and new applications have been indicated. To enumerate the publications of the last few years one would need dozens of pages. On the other hand, many problems of non linear analysis are still far from a solution (problems arising from the internal development of mathematics and, in particular, problems arising in the process of interpreting new problems in the natural sciences). We hope that the English edition of our book will contribute to the further propagation of the ideas of nonlinear analysis.
![Operator Theory and Arithmetic in H [infinity] PDF](https://books.google.com/books/content/images/frontcover/R3fyBwAAQBAJ?fife=w80-h100)
Author: Hari Bercovici
Publisher: American Mathematical Soc.
ISBN: 0821815288
Category : Mathematics
Languages : en
Pages : 289
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Book Description
Jordan's classification theorem for linear transformations on a finite-dimensional vector space is a natural highlight of the deep relationship between linear algebra and the arithmetical properties of polynomial rings. Because the methods and results of finite-dimensional linear algebra seldom extend to or have analogs in infinite-dimensional operator theory, it is therefore remarkable to have a class of operators which has a classification theorem analogous to Jordan's classical result and has properties closely related to the arithmetic of the ring $H^{\infty}$ of bounded analytic functions in the unit disk. $C_0$ is such a class and is the central object of study in this book.A contraction operator belongs to $C_0$ if and only if the associated functional calculus on $H^{\infty}$ has a nontrivial kernel. $C_0$ was discovered by Bela Sz.-Nagy and Ciprian Foias in their work on canonical models for contraction operators on Hilbert space. Besides their intrinsic interest and direct applications, operators of class $C_0$ are very helpful in constructing examples and counterexamples in other branches of operator theory. In addition, $C_0$ arises in certain problems of control and realization theory.In this survey work, the author provides a unified and concise presentation of a subject that was covered in many articles. The book describes the classification theory of $C_0$ and relates this class to other subjects such as general dilation theory, stochastic realization, representations of convolution algebras, and Fredholm theory. This book should be of interest to operator theorists as well as theoretical engineers interested in the applications of operator theory. In an effort to make the book as self-contained as possible, the author gives an introduction to the theory of dilations and functional models for contraction operators. Prerequisites for this book are a course in functional analysis and an acquaintance with the theory of Hardy spaces in the unit disk. In addition, knowledge of the trace class of operators is necessary in the chapter on weak contractions.
Author: Dumitru Motreanu
Publisher: Academic Press
ISBN: 0128133937
Category : Mathematics
Languages : en
Pages : 364
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Book Description
Nonlinear Differential Problems with Smooth and Nonsmooth Constraints systematically evaluates how to solve boundary value problems with smooth and nonsmooth constraints. Primarily covering nonlinear elliptic eigenvalue problems and quasilinear elliptic problems using techniques amalgamated from a range of sophisticated nonlinear analysis domains, the work is suitable for PhD and other early career researchers seeking solutions to nonlinear differential equations. Although an advanced work, the book is self-contained, requiring only graduate-level knowledge of functional analysis and topology. Whenever suitable, open problems are stated and partial solutions proposed. The work is accompanied by end-of-chapter problems and carefully curated references. - Builds from functional analysis and operator theory, to nonlinear elliptic systems and control problems - Outlines the evolution of the main ideas of nonlinear analysis and their roots in classical mathematics - Presented with numerous end-of-chapter exercises and sophisticated open problems - Illustrated with pertinent industrial and engineering numerical examples and applications - Accompanied by hundreds of curated references, saving readers hours of research in conducting literature analysis
Author: Yu Qing Chen
Publisher: Nova Publishers
ISBN: 9781594540677
Category : Mathematics
Languages : en
Pages : 192
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Book Description
This book primarily deals with non-linear operator theory in topological vector spaces and applications. Recently, non-linear functional analysis has become a main field of mathematics, which has played an important role in physics, mechanics and engineering, operations research and economics and many others for the past few decades. The book presents a survey of some main ideas, concepts, methods and applications in non-linear functional analysis.
Author: Jürgen Appell
Publisher: Walter de Gruyter
ISBN: 3110199262
Category : Mathematics
Languages : en
Pages : 421
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Book Description
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.
