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Generalized Inverse Operators

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Generalized Inverse Operators

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Author : Alexander Andreevych Boichuk
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-08-22

Generalized Inverse Operators written by Alexander Andreevych Boichuk 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 2016-08-22 with Mathematics categories.

The book is devoted to the foundations of the theory of boundary-value problems for various classes of systems of differential-operator equations whose linear part is represented by Fredholm operators of the general form. A common point of view on numerous classes of problems that were traditionally studied independently of each other enables us to study, in a natural way, the theory of these problems, to supplement and improve the existing results, and in certain cases, study some of these problems for the first time. With the help of the technique of generalized inverse operators, the Vishik– Lyusternik method, and iterative methods, we perform a detailed investigation of the problems of existence, bifurcations, and branching of the solutions of linear and nonlinear boundary-value problems for various classes of differential-operator systems and propose new procedures for their construction. For more than 11 years that have passed since the appearance of the first edition of the monograph, numerous new publications of the authors in this direction have appeared. In this connection, it became necessary to make some additions and corrections to the previous extensively cited edition, which is still of signifi cant interest for the researchers. For researchers, teachers, post-graduate students, and students of physical and mathematical departments of universities. Contents: Preliminary Information Generalized Inverse Operators in Banach Spaces Pseudoinverse Operators in Hilbert Spaces Boundary-Value Problems for Operator Equations Boundary-Value Problems for Systems of Ordinary Differential Equations Impulsive Boundary-Value Problems for Systems of Ordinary Differential Equations Solutions of Differential and Difference Systems Bounded on the Entire Real Axis

Generalized Inverses Theory And Computations

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Author : Guorong Wang
language : en
Publisher: Springer
Release Date : 2018-05-12

Generalized Inverses Theory And Computations written by Guorong Wang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-12 with Mathematics categories.

This book begins with the fundamentals of the generalized inverses, then moves to more advanced topics. It presents a theoretical study of the generalization of Cramer's rule, determinant representations of the generalized inverses, reverse order law of the generalized inverses of a matrix product, structures of the generalized inverses of structured matrices, parallel computation of the generalized inverses, perturbation analysis of the generalized inverses, an algorithmic study of the computational methods for the full-rank factorization of a generalized inverse, generalized singular value decomposition, imbedding method, finite method, generalized inverses of polynomial matrices, and generalized inverses of linear operators. This book is intended for researchers, postdocs, and graduate students in the area of the generalized inverses with an undergraduate-level understanding of linear algebra.

Generalized Inverses

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Author : Adi Ben-Israel
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18

Generalized Inverses written by Adi Ben-Israel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-18 with Mathematics categories.

This second edition accounts for many major developments in generalized inverses while maintaining the informal and leisurely style of the 1974 first edition. Added material includes a chapter on applications, new exercises, and an appendix on the work of E.H. Moore.

Generalized Inverse Operators

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Author : Alexander Andreevych Boichuk
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-08-22

Classes Of Linear Operators Vol I

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Author : Israel Gohberg
language : en
Publisher: Birkhäuser
Release Date : 2013-03-09

Classes Of Linear Operators Vol I written by Israel Gohberg and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

After the book "Basic Operator Theory" by Gohberg-Goldberg was pub lished, we, that is the present authors, intended to continue with another book which would show the readers the large variety of classes of operators and the important role they play in applications. The book was planned to be of modest size, but due to the profusion of results in this area of analysis, the number of topics grew larger than ex pected. Consequently, we decided to divide the material into two volumes - the first volume being presented now. During the past years, courses and seminars were given at our respective in stitutions based on parts of the texts. These were well received by the audience and enabled us to make appropriate choices for the topics and presentation for the two vol umes. We would like to thank G.J. Groenewald, A.B. Kuijper and A.C.M. Ran of the Vrije Universiteit at Amsterdam, who provided us with lists of remarks and corrections. We are now aware that the Basic Operator Theory book should be revised so that it may suitably fit in with our present volumes. This revision is planned to be the last step of an induction and not the first.

Stable Perturbations Of Operators And Related Topics

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Author : Yifeng Xue
language : en
Publisher: World Scientific
Release Date : 2012-03-16

Stable Perturbations Of Operators And Related Topics written by Yifeng Xue and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-16 with Mathematics categories.

This book provides a broad introduction to the generalized inverses, Moore-Penrose inverses, Drazin inverses and T-S outer generalized inverses and their perturbation analyses in the spaces of infinite-dimensional. This subject has many applications in operator theory, operator algebras, global analysis and approximation theory and so on.Stable Perturbations of Operators and Related Topics is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students. It is also suitable for researchers as a reference. The proofs of statements and explanations in the book are detailed enough that interested readers can study it by themselves./a

Generalized Inverses Of Linear Transformations

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Author : Stephen L. Campbell
language : en
Publisher: SIAM
Release Date : 2009-03-26

Generalized Inverses Of Linear Transformations written by Stephen L. Campbell and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-26 with Mathematics categories.

Provides comprehensive coverage of the mathematical theory of generalized inverses and a wide range of important and practical applications.

Operator Theory Pseudo Differential Equations And Mathematical Physics

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Author : Yuri I. Karlovich
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-30

Operator Theory Pseudo Differential Equations And Mathematical Physics written by Yuri I. Karlovich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-30 with Mathematics categories.

This volume is a collection of papers devoted to the 70th birthday of Professor Vladimir Rabinovich. The opening article (by Stefan Samko) includes a short biography of Vladimir Rabinovich, along with some personal recollections and bibliography of his work. It is followed by twenty research and survey papers in various branches of analysis (pseudodifferential operators and partial differential equations, Toeplitz, Hankel, and convolution type operators, variable Lebesgue spaces, etc.) close to Professor Rabinovich's research interests. Many of them are written by participants of the International workshop “Analysis, Operator Theory, and Mathematical Physics” (Ixtapa, Mexico, January 23–27, 2012) having a long history of scientific collaboration with Vladimir Rabinovich, and are partially based on the talks presented there.The volume will be of great interest to researchers and graduate students in differential equations, operator theory, functional and harmonic analysis, and mathematical physics.

Spectral Theory Of Linear Operators And Spectral Systems In Banach Algebras

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Author : Vladimir Müller
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11

Spectral Theory Of Linear Operators And Spectral Systems In Banach Algebras written by Vladimir Müller and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.

Spectral theory is an important part of functional analysis.It has numerous appli cations in many parts of mathematics and physics including matrix theory, func tion theory, complex analysis, differential and integral equations, control theory and quantum physics. In recent years, spectral theory has witnessed an explosive development. There are many types of spectra, both for one or several commuting operators, with important applications, for example the approximate point spectrum, Taylor spectrum, local spectrum, essential spectrum, etc. The present monograph is an attempt to organize the available material most of which exists only in the form of research papers scattered throughout the literature. The aim is to present a survey of results concerning various types of spectra in a unified, axiomatic way. The central unifying notion is that of a regularity, which in a Banach algebra is a subset of elements that are considered to be "nice". A regularity R in a Banach algebra A defines the corresponding spectrum aR(a) = {A E C : a - ,\ rJ. R} in the same way as the ordinary spectrum is defined by means of invertible elements, a(a) = {A E C : a - ,\ rJ. Inv(A)}. Axioms of a regularity are chosen in such a way that there are many natural interesting classes satisfying them. At the same time they are strong enough for non-trivial consequences, for example the spectral mapping theorem.

Operator And Norm Inequalities And Related Topics

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Author : Richard M. Aron
language : en
Publisher: Springer Nature
Release Date : 2022-08-10

Operator And Norm Inequalities And Related Topics written by Richard M. Aron and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-10 with Mathematics categories.

Inequalities play a central role in mathematics with various applications in other disciplines. The main goal of this contributed volume is to present several important matrix, operator, and norm inequalities in a systematic and self-contained fashion. Some powerful methods are used to provide significant mathematical inequalities in functional analysis, operator theory and numerous fields in recent decades. Some chapters are devoted to giving a series of new characterizations of operator monotone functions and some others explore inequalities connected to log-majorization, relative operator entropy, and the Ando-Hiai inequality. Several chapters are focused on Birkhoff–James orthogonality and approximate orthogonality in Banach spaces and operator algebras such as C*-algebras from historical perspectives to current development. A comprehensive account of the boundedness, compactness, and restrictions of Toeplitz operators can be found in the book. Furthermore, an overview of the Bishop-Phelps-Bollobás theorem is provided. The state-of-the-art of Hardy-Littlewood inequalities in sequence spaces is given. The chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.

Generalized Inverse Operators

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