Generalized Inverse Operators

Author : Alexander Andreevych Boichuk,Anatolii M. Samoilenko
Publisher : Walter de Gruyter GmbH & Co KG
Page : 314 pages
File Size : 49,9 Mb
Release : 2016-08-22
Category : Mathematics
ISBN : 9783110387353

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Generalized Inverse Operators by Alexander Andreevych Boichuk,Anatolii M. Samoilenko Pdf

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

Author : Alexander Andreevych Boichuk,Anatolii M. Samoilenko
Publisher : Walter de Gruyter GmbH & Co KG
Page : 314 pages
File Size : 40,8 Mb
Release : 2016-08-22
Category : Mathematics
ISBN : 9783110378443

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Generalized Inverse Operators by Alexander Andreevych Boichuk,Anatolii M. Samoilenko Pdf

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

Author : Alexander Andreevych Boichuk,Anatolii M. Samoilenko
Publisher : Unknown
Page : 320 pages
File Size : 41,5 Mb
Release : 2016
Category : Electronic
ISBN : 3110378450

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Generalized Inverse Operators by Alexander Andreevych Boichuk,Anatolii M. Samoilenko Pdf

Author : A. A. Bojčuk,A. M. Samojlenko
Publisher : Walter de Gruyter
Page : 317 pages
File Size : 48,7 Mb
Release : 2004-01-01
Category : Electronic
ISBN : 3111826910

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Generalized Inverse Operators and Fredholm Boundary-Value Problems by A. A. Bojčuk,A. M. Samojlenko Pdf

The authors of this monograph suggest some methods for the construction of the generalized inverse (or pseudo-inverse) operators for the original linear Fredholm operators in Banach (or Hilbert) spaces for boundary-value problems regarded as operator systems in abstract spaces. They also study basic properties of the generalized Green's operator.

Author : Adi Ben-Israel,Thomas N.E. Greville
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 45,8 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387216348

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Generalized Inverses by Adi Ben-Israel,Thomas N.E. Greville Pdf

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.

Author : Guorong Wang,Yimin Wei,Sanzheng Qiao
Publisher : Springer
Page : 378 pages
File Size : 46,9 Mb
Release : 2018-05-12
Category : Mathematics
ISBN : 9789811301469

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Generalized Inverses: Theory and Computations by Guorong Wang,Yimin Wei,Sanzheng Qiao Pdf

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.

Author : Dragana S. Cvetković‐Ilić,Yimin Wei
Publisher : Springer
Page : 194 pages
File Size : 43,5 Mb
Release : 2017-10-07
Category : Mathematics
ISBN : 9789811063497

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Algebraic Properties of Generalized Inverses by Dragana S. Cvetković‐Ilić,Yimin Wei Pdf

This book addresses selected topics in the theory of generalized inverses. Following a discussion of the “reverse order law” problem and certain problems involving completions of operator matrices, it subsequently presents a specific approach to solving the problem of the reverse order law for {1} -generalized inverses. Particular emphasis is placed on the existence of Drazin invertible completions of an upper triangular operator matrix; on the invertibility and different types of generalized invertibility of a linear combination of operators on Hilbert spaces and Banach algebra elements; on the problem of finding representations of the Drazin inverse of a 2x2 block matrix; and on selected additive results and algebraic properties for the Drazin inverse. In addition to the clarity of its content, the book discusses the relevant open problems for each topic discussed. Comments on the latest references on generalized inverses are also included. Accordingly, the book will be useful for graduate students, PhD students and researchers, but also for a broader readership interested in these topics.

Author : M. Zuhair Nashed
Publisher : Elsevier
Page : 1069 pages
File Size : 55,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483270296

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Generalized Inverses and Applications by M. Zuhair Nashed Pdf

Generalized Inverses and Applications, contains the proceedings of an Advanced Seminar on Generalized Inverses and Applications held at the University of Wisconsin-Madison on October 8-10, 1973 under the auspices of the university's Mathematics Research Center. The seminar provided a forum for discussing the basic theory of generalized inverses and their applications to analysis and operator equations. Numerical analysis and approximation methods are considered, along with applications to statistics and econometrics, optimization, system theory, and operations research. Comprised of 14 chapters, this book begins by describing a unified approach to generalized inverses of linear operators, with particular reference to algebraic, topological, extremal, and proximinal properties. The reader is then introduced to the algebraic aspects of the generalized inverse of a rectangular matrix; the Fredholm pseudoinverse; and perturbations and approximations for generalized inverses and linear operator equations. Subsequent chapters deal with various applications of generalized inverses, including programming, games, and networks, as well as estimation and aggregation in econometrics. This monograph will be of interest to mathematicians and students of mathematics.

Author : P.L. Butzer,E. Gärlich,B. Szökefalvi-Nagy
Publisher : Birkhäuser
Page : 461 pages
File Size : 50,5 Mb
Release : 2013-03-07
Category : Mathematics
ISBN : 9783034893695

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Functional Analysis and Approximation by P.L. Butzer,E. Gärlich,B. Szökefalvi-Nagy Pdf

These Proceedings form a record of the lectures presented at the interna tional Conference on Functional Analysis and Approximation held at the Ober wolfach Mathematical Research Institute, August 9-16, 1980. They include 33 of the 38 invited conference papers, as well as three papers subsequently submitted in writing. Further, there is a report devoted to new and unsolved problems, based on two special sessions of the conference. The present volume is the sixth Oberwolfach Conference in Birkhauser's ISNM series to be edited at Aachen *. It is once again devoted to more significant results obtained in the wide areas of approximation theory, harmonic analysis, functional analysis, and operator theory during the past three years. Many of the papers solicited not only outline fundamental advances in their fields but also focus on interconnections between the various research areas. The papers in the present volume have been grouped into nine chapters. Chapter I, on operator theory, deals with maps on positive semidefinite opera tors, spectral bounds of semigroup operators, evolution equations of diffusion type, the spectral theory of propagators, and generalized inverses. Chapter II, on functional analysis, contains papers on modular approximation, interpolation spaces, and unconditional bases.

Author : Israel Gohberg,Seymor Goldberg,Marinus Kaashoek
Publisher : Birkhäuser
Page : 479 pages
File Size : 44,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783034875097

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Classes of Linear Operators Vol. I by Israel Gohberg,Seymor Goldberg,Marinus Kaashoek Pdf

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.

Author : Yifeng Xue
Publisher : World Scientific
Page : 304 pages
File Size : 49,6 Mb
Release : 2012-03-16
Category : Mathematics
ISBN : 9789814452809

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Stable Perturbations of Operators and Related Topics by Yifeng Xue Pdf

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. Contents:Basics in Functional AnalysisStable Perturbation of Densely-Defined Closed OperatorsMoore–Penrose Inverse and Its Stable PerturbationDrazin Inverses, T–S Generalized Inverses and Their PerturbationsMiscellaneous ApplicationsSome Related Topics Readership: Graduate students and researchers in analysis and differential equations, numerical analysis and computational mathematics, algebra. Keywords:Generalized Inverse;Moore–Penrose Inverse;Drazin Inverse;Stable PerturbationKey Features:The stable perturbation theory of generalized inverses, Drazin inverses and index of a Fredholm element relative to a homomorphismare are of unique interest in this book The stable perturbation theory of generalized inverses is a very useful tool in studying the perturbations of Moore–Penrose inverses and Drazin inverses. It also has important applications in Operator Theory, Operator Algebras and Global Analysis. All these are described completely in the bookThe expression and index of the perturbed Drazin inverse of a Drazin invertible operator or element under stable perturbation are very useful in computing the Drazin inverses of certain operators and elements and estimating the error-bounds of the perturbations. It can not be found in current books concerning the Drazin inversesThe Toeplitz operator and its index is a very interesting topic in the Mathematical World. In this book, we define a generalized Toeplitz element in a Banach algebra and establish its index formula. Using it, we can deduce the indices formulae of some classical Toeplitz operators. This theory is new and very usefulReviews: "This book may be of some interest to specialists." Zentralblatt MATH

Author : Yuri I. Karlovich,Luigi Rodino,Bernd Silbermann,Ilya M. Spitkovsky
Publisher : Springer Science & Business Media
Page : 410 pages
File Size : 41,6 Mb
Release : 2012-10-30
Category : Mathematics
ISBN : 9783034805377

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Operator Theory, Pseudo-Differential Equations, and Mathematical Physics by Yuri I. Karlovich,Luigi Rodino,Bernd Silbermann,Ilya M. Spitkovsky Pdf

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.​

Author : Stephen L. Campbell,Carl D. Meyer
Publisher : SIAM
Page : 288 pages
File Size : 53,8 Mb
Release : 2009-03-26
Category : Mathematics
ISBN : 9780898716719

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Generalized Inverses of Linear Transformations by Stephen L. Campbell,Carl D. Meyer Pdf

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

Author : Schroder
Publisher : Academic Press
Page : 366 pages
File Size : 41,5 Mb
Release : 1980-09-01
Category : Computers
ISBN : 9780080956558

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Operator Inequalities by Schroder Pdf

Operator Inequalities

Author : Richard M. Aron,Mohammad Sal Moslehian,Ilya M. Spitkovsky,Hugo J. Woerdeman
Publisher : Springer Nature
Page : 822 pages
File Size : 50,9 Mb
Release : 2022-08-10
Category : Mathematics
ISBN : 9783031021046

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Operator and Norm Inequalities and Related Topics by Richard M. Aron,Mohammad Sal Moslehian,Ilya M. Spitkovsky,Hugo J. Woerdeman Pdf

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.