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On Triangular Representation Of A Class Of Linear Operators
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Book Synopsis Triangular and Jordan Representations of Linear Operators by : M. S. Brodskii
Download or read book Triangular and Jordan Representations of Linear Operators written by M. S. Brodskii and published by American Mathematical Soc.. This book was released on 1971 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Determining the invariant subspaces of any given transformation and writing the transformation as an integral in terms of invariant subspaces is a fundamental problem. This book presents the foundations of the theory of triangular and Jordan representations of bounded linear operators in Hilbert space and solves the problem in the case of completely continuous transformations. The reader is assumed to know the basics of linear operator theory.
Book Synopsis Classes of Linear Operators by : Israel Gohberg
Download or read book Classes of Linear Operators written by Israel Gohberg and published by Birkhäuser. This book was released on 2013-03-09 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: These two volumes constitute texts for graduate courses in linear operator theory. The reader is assumed to have a knowledge of both complex analysis and the first elements of operator theory. The texts are intended to concisely present a variety of classes of linear operators, each with its own character, theory, techniques and tools. For each of the classes, various differential and integral operators motivate or illustrate the main results. Although each class is treated seperately and the first impression may be that of many different theories, interconnections appear frequently and unexpectedly. The result is a beautiful, unified and powerful theory. The classes we have chosen are representatives of the principal important classes of operators, and we believe that these illustrate the richness of operator theory, both in its theoretical developments and in its applicants. Because we wanted the books to be of reasonable size, we were selective in the classes we chose and restricted our attention to the main features of the corresponding theories. However, these theories have been updated and enhanced by new developments, many of which appear here for the first time in an operator-theory text. In the selection of the material the taste and interest of the authors played an important role.
Book Synopsis Encyclopedic Dictionary of Mathematics by : Nihon Sūgakkai
Download or read book Encyclopedic Dictionary of Mathematics written by Nihon Sūgakkai and published by MIT Press. This book was released on 1993 with total page 1180 pages. Available in PDF, EPUB and Kindle. Book excerpt: V.1. A.N. v.2. O.Z. Apendices and indexes.
Book Synopsis Special Classes of Linear Operators and Other Topics by : G. Arsene
Download or read book Special Classes of Linear Operators and Other Topics written by G. Arsene and published by Birkhäuser. This book was released on 2012-12-06 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Operator Theory conferences, organized by the Department of Mathematics of INCREST and the University of Timi~oara, are conceived as a means to promote cooperation and exchange of information between specialists in all areas of operator theory. This volume consists of a careful selec£ion of papers contributed by the participants of the 1986 Conference. They reflect most of the topics dealt with by the modern operator theory, including recent advances in dual operator algebras and the fnvariant subspace problem, operators in indefinite metric spaces, hyponormal, quasi triangular and decomposable operators, various problems in C*- and W*-algebras and so on. The research contracts of the Department of Mathematics of INCREST with the National Council for Science and Technology of Romania provided the means for developing the research activity in mathematics; they represent the generous framework of these meetings, too. It is our pleasure to acknowledge the financial support of UNESCO which also contributed to the success of this meeting. We are indebted to Professor Israel Gohberg for including these Proceedings in the OT Series and for valuable advice in the editing process. Birkhiiuser Verlag was very cooperative in publishing this volume. Camelia Minculescu, Iren Nemethi and Rodica Stoenescu dealt with the dif ficult task of typing the whOle manuscript using a Rank Xerox 860 word processor; we thank them for the excellent job they did.
Book Synopsis Linear Algebra by : Meighan I. Dillon
Download or read book Linear Algebra written by Meighan I. Dillon and published by American Mathematical Society. This book was released on 2022-10-14 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is directed towards students who are familiar with matrices and their use in solving systems of linear equations. The emphasis is on the algebra supporting the ideas that make linear algebra so important, both in theoretical and practical applications. The narrative is written to bring along students who may be new to the level of abstraction essential to a working understanding of linear algebra. The determinant is used throughout, placed in some historical perspective, and defined several different ways, including in the context of exterior algebras. The text details proof of the existence of a basis for an arbitrary vector space and addresses vector spaces over arbitrary fields. It develops LU-factorization, Jordan canonical form, and real and complex inner product spaces. It includes examples of inner product spaces of continuous complex functions on a real interval, as well as the background material that students may need in order to follow those discussions. Special classes of matrices make an entrance early in the text and subsequently appear throughout. The last chapter of the book introduces the classical groups.
Book Synopsis Basic Classes of Linear Operators by : Israel Gohberg
Download or read book Basic Classes of Linear Operators written by Israel Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive graduate textbook that introduces functional analysis with an emphasis on the theory of linear operators and its application to differential equations, integral equations, infinite systems of linear equations, approximation theory, and numerical analysis. As a textbook designed for senior undergraduate and graduate students, it begins with the geometry of Hilbert spaces and proceeds to the theory of linear operators on these spaces including Banach spaces. Presented as a natural continuation of linear algebra, the book provides a firm foundation in operator theory which is an essential part of mathematical training for students of mathematics, engineering, and other technical sciences.
Book Synopsis Classes of Linear Operators Vol. I by : Israel Gohberg
Download or read book Classes of Linear Operators Vol. I written by Israel Gohberg and published by Birkhäuser. This book was released on 2013-03-09 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Operator Approach to Linear Control Systems by : A. Cheremensky
Download or read book Operator Approach to Linear Control Systems written by A. Cheremensky and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of optimization runs through most parts of control theory. The simplest optimal controls are preplanned (programmed) ones. The problem of constructing optimal preplanned controls has been extensively worked out in literature (see, e. g. , the Pontrjagin maximum principle giving necessary conditions of preplanned control optimality). However, the concept of op timality itself has a restrictive character: it is limited by what one means under optimality in each separate case. The internal contradictoriness of the preplanned control optimality ("the better is the enemy of the good") yields that the practical significance of optimal preplanned controls proves to be not great: such controls are usually sensitive to unregistered disturbances (includ ing the round-off errors which are inevitable when computer devices are used for forming controls), as there is the effect of disturbance accumulation in the control process which makes controls to be of little use on large time inter vals. This gap is mainly provoked by oversimplified settings of optimization problems. The outstanding result of control theory established in the end of the first half of our century is that controls in feedback form ensure the weak sensitivity of closed loop systems with respect to "small" unregistered internal and external disturbances acting in them (here we do not need to discuss performance indexes, since the considered phenomenon is of general nature). But by far not all optimal preplanned controls can be represented in a feedback form.
Book Synopsis Operator Theory and Related Topics by : V.M. Adamyan
Download or read book Operator Theory and Related Topics written by V.M. Adamyan and published by Birkhäuser. This book was released on 2012-12-06 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is the second of the two volume Proceedings of the Mark Krein International Conference on Operator Theory and Applications. This conference, which was dedicated to the 90th Anniversary of the prominent mathematician Mark Krein, was held in Odessa, Ukraine from 18-22 August, 1997. The conference focused on the main ideas, methods, results, and achievements of M. G. Krein. This second volume is devoted to operator theory and related topics. It opens with the bibliography of M. G. Krein and a number of survey papers about his work. The main part of the book consists of original research papers presenting the state of the art in operator theory and its applications. The first volume of these proceedings, entitled Differential Operators and related Topics, concerns the other aspects of the conference. The two volumes will be of interest to a wide-range of readership in pure and applied mathematics, physics and engineering sciences. Table of Contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Bibliography of Mark Grigorevich Krein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Review papers: M. G. Krein's Contributions to Prediction Theory H. Dym M. G. Krein's Contribution to the Moment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 AA Nudelman Research Papers: Solution of the Truncated Matrix Hamburger Moment Problem according to M. G. Krein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Y. M. Adamyan and I. M. Tkachenko Extreme Points of a Positive Operator Ball . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 T. Ando M-accretive Extensions of Sectorial Operators and Krein Spaces . . . . . . . . . 67 Y. M. Arlinskii A Simple Proof of the Continuous Commutant Lifting Theorem . . . . . . . . . . 83 R. Bruzual and M.
Book Synopsis Linear Algebra: by : Saikia, Promode Kumar
Download or read book Linear Algebra: written by Saikia, Promode Kumar and published by Pearson Education India. This book was released on with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Algebra is designed for postgraduate and undergraduate students of Mathematics. This book explains the basics comprehensively and with clarity. The flowing narrative of the book provides a refreshing approach to the subject. Drawing on decad
Book Synopsis Operator Theory and Arithmetic in H [infinity] by : Hari Bercovici
Download or read book Operator Theory and Arithmetic in H [infinity] written by Hari Bercovici and published by American Mathematical Soc.. This book was released on 1988 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Book Synopsis History of Banach Spaces and Linear Operators by : Albrecht Pietsch
Download or read book History of Banach Spaces and Linear Operators written by Albrecht Pietsch and published by Springer Science & Business Media. This book was released on 2007-12-31 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.
Book Synopsis Harmonic Analysis of Operators on Hilbert Space by : Béla Sz Nagy
Download or read book Harmonic Analysis of Operators on Hilbert Space written by Béla Sz Nagy and published by Springer Science & Business Media. This book was released on 2010-09-01 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.
Book Synopsis Orthogonal Matrix-valued Polynomials and Applications by : I. Gohberg
Download or read book Orthogonal Matrix-valued Polynomials and Applications written by I. Gohberg and published by Birkhäuser. This book was released on 2013-11-21 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is a largely expository account of the theory of p x p matrix polyno mials associated with Hermitian block Toeplitz matrices and some related problems of interpolation and extension. Perhaps the main novelty is the use of reproducing kernel Pontryagin spaces to develop parts of the theory in what hopefully the reader will regard as a reasonably lucid way. The topics under discussion are presented in a series of short sections, the headings of which give a pretty good idea of the overall contents of the paper. The theory is a rich one and the present paper in spite of its length is far from complete. The author hopes to fill in some of the gaps in future publications. The story begins with a given sequence h_n" ... , hn of p x p matrices with h-i = hj for j = 0, ... , n. We let k = O, ... ,n, (1.1) denote the Hermitian block Toeplitz matrix based on ho, ... , hk and shall denote its 1 inverse H k by (k)] k [ r = .. k = O, ... ,n, (1.2) k II} . '-0 ' I- whenever Hk is invertible.
Book Synopsis Studies in Memory of Issai Schur by : Anthony Joseph
Download or read book Studies in Memory of Issai Schur written by Anthony Joseph and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume Studies in Memory of Issai Schur was conceived as a tribute to Schur's of his tragic end. His impact on great contributions to mathematics and in remembrance of mathematicians Representation Theory alone was so great that a significant number of Researchers (TMR) Network, in the European Community Training and Mobility Orbits, Crystals and Representation Theory, in operation during the period (1997-2002) have been occupied with what has been called Schur theory. Consequently, this volume has the additional purpose of recording some of the significant results of the network. It was furthermore appropriate that invited contributors should be amongst the speakers at the Paris Midterm Workshop of the network held at Chevaleret during 21-25 May, 2000 as well as those of the Schur Memoriam Workshop held at the Weizmann Institute, Rehovot, during 27-31 December 2000. The latter marked the sixtieth anniversary of Schur's passing and took place in the 125th year of his birth.
Book Synopsis Spectral Theory and Wave Processes by : M. Sh. Birman
Download or read book Spectral Theory and Wave Processes written by M. Sh. Birman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this collection are devoted to various problems in mathematical physics and mathematical analysis, primarily in the fields of spectral theory and the theory of wave processes. The collection is intended for mathematicians sPf>cializing in the fields of mathematical physics, functional analysis, and the theory of differential equations. In addition, it is of some interest to theoretical physicists. The first paper deals with a mixed boundary value problem for a system of elasticity equations, and considers fields in the neighborhood of various wave fronts. The method used permits an estimate of the errors in the Ben-Menahem approximate method. Paper 2 investigates operators in separable Hilbert space given by double integrals of a type defined at the beginning of the paper, and in which integration is understood as the limit of the integral sums of Riemann-stieltjes. In paper 3, the problem of calculation of elastic constants for a laminarly inhomogeneous semi-infinite medium is conSidered, and the uniqueness of the solution of the inverse seismic problem at finite depth proved. The fourth paper gives a detailed account of the results of an earlier paper by the same author, in which he generalized to the three-dimensional case the trace formulas obtained for the one-dimensional Schroedinger operator. Asymptotic estimates of the resolvent kernel and solutions of the scattering problem are given.
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