Download or read book On Spectral Decompositions of Operators in J space written by Väinö Jalava and published by . This book was released on 1969 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Decompositions on Banach Spaces written by I. Erdelyi and published by Springer. This book was released on 2006-11-15 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analytic Functional Calculus and Spectral Decompositions written by Florian-Horia Vasilescu and published by Springer Science & Business Media. This book was released on 1983-01-31 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Decompositions and Analytic Sheaves written by Jörg Eschmeier and published by Oxford University Press. This book was released on 1996 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rapid developments in multivariable spectral theory have led to important and fascinating results which also have applications in other mathematical disciplines. In this book, various concepts from function theory and complex analytic geometry are drawn together to give a new approach to concrete spectral computations and give insights into new developments in the spectral theory of linear operators. Classical results from cohomology theory of Banach algebras, multidimensional spectral theory, and complex analytic geometry have been freshly interpreted using the language of homological algebra. The advantages of this approach are illustrated by a variety of examples, unexpected applications, and conceptually new ideas that should stimulate further research among mathematicians.
Download or read book Spectral Theory of Operators on Hilbert Spaces written by Carlos S. Kubrusly and published by Springer Science & Business Media. This book was released on 2012-06-01 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introductory textbook for a first graduate course in the subject. The coverage of topics is thorough, as the book explores various delicate points and hidden features often left untreated. Spectral Theory of Operators on Hilbert Spaces is addressed to an interdisciplinary audience of graduate students in mathematics, statistics, economics, engineering, and physics. It will also be useful to working mathematicians using spectral theory of Hilbert space operators, as well as for scientists wishing to apply spectral theory to their field.
Download or read book Introduction to the Spectral Theory of Operators in Spaces with an Indefinite Metric written by I. S. Iohvidov and published by Walter de Gruyter GmbH & Co KG. This book was released on 1983-01-14 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Introduction to the Spectral Theory of Operators in Spaces with an Indefinite Metric".
Download or read book Multivariable Operator Theory written by Ernst Albrecht and published by Springer Nature. This book was released on 2024-01-22 with total page 893 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Jörg Eschmeier made a number of fundamental contributions to the development of operator theory and related topics. The chapters in this volume, compiled in his memory, are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.
Download or read book The Diversity and Beauty of Applied Operator Theory written by Albrecht Böttcher and published by Springer. This book was released on 2018-04-27 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents 29 invited articles written by participants of the International Workshop on Operator Theory and its Applications held in Chemnitz in 2017. The contributions include both expository essays and original research papers illustrating the diversity and beauty of insights gained by applying operator theory to concrete problems. The topics range from control theory, frame theory, Toeplitz and singular integral operators, Schrödinger, Dirac, and Kortweg-de Vries operators, Fourier integral operator zeta-functions, C*-algebras and Hilbert C*-modules to questions from harmonic analysis, Monte Carlo integration, Fibonacci Hamiltonians, and many more. The book offers researchers in operator theory open problems from applications that might stimulate their work and shows those from various applied fields, such as physics, engineering, or numerical mathematics how to use the potential of operator theory to tackle interesting practical problems.
Download or read book Elementary Operator Theory written by Marat V. Markin and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-04-06 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is intended as a text for a one-semester graduate course in operator theory to be taught "from scratch'', not as a sequel to a functional analysis course, with the basics of the spectral theory of linear operators taking the center stage. The book consists of six chapters and appendix, with the material flowing from the fundamentals of abstract spaces (metric, vector, normed vector, and inner product), the Banach Fixed-Point Theorem and its applications, such as Picard's Existence and Uniqueness Theorem, through the basics of linear operators, two of the three fundamental principles (the Uniform Boundedness Principle and the Open Mapping Theorem and its equivalents: the Inverse Mapping and Closed Graph Theorems), to the elements of the spectral theory, including Gelfand's Spectral Radius Theorem and the Spectral Theorem for Compact Self-Adjoint Operators, and its applications, such as the celebrated Lyapunov Stability Theorem. Conceived as a text to be used in a classroom, the book constantly calls for the student's actively mastering the knowledge of the subject matter. There are problems at the end of each chapter, starting with Chapter 2 and totaling at 150. Many important statements are given as problems and frequently referred to in the main body. There are also 432 Exercises throughout the text, including Chapter 1 and the Appendix, which require of the student to prove or verify a statement or an example, fill in certain details in a proof, or provide an intermediate step or a counterexample. They are also an inherent part of the material. More difficult problems are marked with an asterisk, many problems and exercises are supplied with "existential'' hints. The book is generous on Examples and contains numerous Remarks accompanying definitions, examples, and statements to discuss certain subtleties, raise questions on whether the converse assertions are true, whenever appropriate, or whether the conditions are essential. With carefully chosen material, proper attention given to applications, and plenty of examples, problems, and exercises, this well-designed text is ideal for a one-semester Master's level graduate course in operator theory with emphasis on spectral theory for students majoring in mathematics, physics, computer science, and engineering. Contents Preface Preliminaries Metric Spaces Vector Spaces, Normed Vector Spaces, and Banach Spaces Linear Operators Elements of Spectral Theory in a Banach Space Setting Elements of Spectral Theory in a Hilbert Space Setting Appendix: The Axiom of Choice and Equivalents Bibliography Index
Download or read book Banach Space Complexes written by C.-G. Ambrozie and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this work is to initiate a systematic study of those properties of Banach space complexes that are stable under certain perturbations. A Banach space complex is essentially an object of the form 1 op-l oP +1 ... --+ XP- --+ XP --+ XP --+ ... , where p runs a finite or infiniteinterval ofintegers, XP are Banach spaces, and oP : Xp ..... Xp+1 are continuous linear operators such that OPOp-1 = 0 for all indices p. In particular, every continuous linear operator S : X ..... Y, where X, Yare Banach spaces, may be regarded as a complex: O ..... X ~ Y ..... O. The already existing Fredholm theory for linear operators suggested the possibility to extend its concepts and methods to the study of Banach space complexes. The basic stability properties valid for (semi-) Fredholm operators have their counterparts in the more general context of Banach space complexes. We have in mind especially the stability of the index (i.e., the extended Euler characteristic) under small or compact perturbations, but other related stability results can also be successfully extended. Banach (or Hilbert) space complexes have penetrated the functional analysis from at least two apparently disjoint directions. A first direction is related to the multivariable spectral theory in the sense of J. L.
Download or read book Encyclopaedia of Mathematics set written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 1994-02-28 with total page 982 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Encyclopaedia of Mathematics is the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics which exists today. With over 7,000 articles from `A-integral' to `Zygmund Class of Functions', supplemented with a wealth of complementary information, and an index volume providing thorough cross-referencing of entries of related interest, the Encyclopaedia of Mathematics offers an immediate source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods. The depth and breadth of content and the straightforward, careful presentation of the information, with the emphasis on accessibility, makes the Encyclopaedia of Mathematics an immensely useful tool for all mathematicians and other scientists who use, or are confronted by, mathematics in their work. The Enclyclopaedia of Mathematics provides, without doubt, a reference source of mathematical knowledge which is unsurpassed in value and usefulness. It can be highly recommended for use in libraries of universities, research institutes, colleges and even schools.
Download or read book Function Spaces written by Krzysztof Jarosz and published by American Mathematical Soc.. This book was released on 2007 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of contributions by the participants of the Fifth Conference on Function Spaces, held at Southern Illinois University in May of 2006. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), $L{p $-spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects. The goal of the conference was to bring together mathematicians interested in various problems related to function spaces and to facilitate the exchange of ideas between people working on similar problems. Hence, the majority of papers in this book are accessible to non-experts. Some articles contain expositions of known results and discuss open problems, others contain new results.
Download or read book Operator Extensions Interpolation of Functions and Related Topics written by Aurelian Gheondea and published by Springer Science & Business Media. This book was released on 1993 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: On Some Operator Colligations and Associated Reproducing Kernel Spaces.- On the Spectra of Selfadjoint Extensions.- On the Spectrum of Singular Nonselfadjoint Differential Operators.- The Commutant Lifting Theorem for Contractions on Kre?n Spaces.- A Method for Constructing Invariant Subspaces for some Operators on Kre?n Spaces.- Applications of the Furuta Inequality to Operator Inequalities and Norm Inequalities Preserving some Orders.- Quasi-contractions on Kre?n Spaces.- Antitonicity of the Inverse and J-Contractivity.- Unitary Extensions of a System of Commuting Isometric Operators.- Some Generalizations of Classical Interpolation Problems.- The Kobayashi Distance between two Contractions.- The Category of Quotient Bornological Spaces.
Download or read book Complex Analysis and Dynamical Systems III written by Mark Lʹvovich Agranovskiĭ and published by American Mathematical Soc.. This book was released on 2008 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume cover a wide variety of topics in the geometric theory of functions of one and several complex variables, including univalent functions, conformal and quasiconformal mappings, minimal surfaces, and dynamics in infinite-dimensional spaces. In addition, there are several articles dealing with various aspects of approximation theory and partial differential equations. Taken together, the articles collected here provide the reader with a panorama of activity in complex analysis, drawn by a number of leading figures in the field.
Download or read book Spectral Theory of Bounded Linear Operators written by Carlos S. Kubrusly and published by Springer Nature. This book was released on 2020-01-30 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces spectral theory for bounded linear operators by focusing on (i) the spectral theory and functional calculus for normal operators acting on Hilbert spaces; (ii) the Riesz-Dunford functional calculus for Banach-space operators; and (iii) the Fredholm theory in both Banach and Hilbert spaces. Detailed proofs of all theorems are included and presented with precision and clarity, especially for the spectral theorems, allowing students to thoroughly familiarize themselves with all the important concepts. Covering both basic and more advanced material, the five chapters and two appendices of this volume provide a modern treatment on spectral theory. Topics range from spectral results on the Banach algebra of bounded linear operators acting on Banach spaces to functional calculus for Hilbert and Banach-space operators, including Fredholm and multiplicity theories. Supplementary propositions and further notes are included as well, ensuring a wide range of topics in spectral theory are covered. Spectral Theory of Bounded Linear Operators is ideal for graduate students in mathematics, and will also appeal to a wider audience of statisticians, engineers, and physicists. Though it is mostly self-contained, a familiarity with functional analysis, especially operator theory, will be helpful.
Download or read book Quaternionic de Branges Spaces and Characteristic Operator Function written by Daniel Alpay and published by Springer Nature. This book was released on 2020-01-27 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work contributes to the study of quaternionic linear operators. This study is a generalization of the complex case, but the noncommutative setting of quaternions shows several interesting new features, see e.g. the so-called S-spectrum and S-resolvent operators. In this work, we study de Branges spaces, namely the quaternionic counterparts of spaces of analytic functions (in a suitable sense) with some specific reproducing kernels, in the unit ball of quaternions or in the half space of quaternions with positive real parts. The spaces under consideration will be Hilbert or Pontryagin or Krein spaces. These spaces are closely related to operator models that are also discussed. The focus of this book is the notion of characteristic operator function of a bounded linear operator A with finite real part, and we address several questions like the study of J-contractive functions, where J is self-adjoint and unitary, and we also treat the inverse problem, namely to characterize which J-contractive functions are characteristic operator functions of an operator. In particular, we prove the counterpart of Potapov's factorization theorem in this framework. Besides other topics, we consider canonical differential equations in the setting of slice hyperholomorphic functions and we define the lossless inverse scattering problem. We also consider the inverse scattering problem associated with canonical differential equations. These equations provide a convenient unifying framework to discuss a number of questions pertaining, for example, to inverse scattering, non-linear partial differential equations and are studied in the last section of this book.
Download or read book Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras written by Vladimir Müller and published by Birkhäuser. This book was released on 2013-11-11 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. Many results appear here for the first time in a monograph.
