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Analytic Functional Calculus And Spectral Decompositions
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Author :Florian-Horia Vasilescu Publisher :Springer Science & Business Media ISBN 13 :9789027713766 Total Pages :398 pages Book Rating :4.7/5 (137 download)
Book Synopsis Analytic Functional Calculus and Spectral Decompositions by : Florian-Horia Vasilescu
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:
Book Synopsis Spectral Decompositions and Analytic Sheaves by : Jörg Eschmeier
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.
Book Synopsis New Approaches in Spectral Decomposition by : Ridgley Lange
Download or read book New Approaches in Spectral Decomposition written by Ridgley Lange and published by American Mathematical Soc.. This book was released on 1992 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at a general mathematical audience, this book provides a careful exposition of developments in the theory of spectral decomposition. Bringing the reader from the basics up to the level of current research in the area at the time of writing, Lange and Wang present an accessible account of the techniques used in the theory and applications of decomposable operators and related classes of operators. The book begins with a discussion of criteria for decomposable and related types of operators, and an analysis that relates and distinguishes among them. Perturbation theory of decomposable and other operators, applications to classical Hilberty space operators, quasisimilarity, and a new class of weakly decomposable operators are also discussed. The book closes with an exposition of some classical theories on invariant subspaces for subdecomposable and hyponormal operators, and a presentation of the parallel spectral theory of commuting systems.
Book Synopsis Spectral Properties of Noncommuting Operators by : Brian Jefferies
Download or read book Spectral Properties of Noncommuting Operators written by Brian Jefferies and published by Springer Science & Business Media. This book was released on 2004-05-13 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Forming functions of operators is a basic task of many areas of linear analysis and quantum physics. Weyl’s functional calculus, initially applied to the position and momentum operators of quantum mechanics, also makes sense for finite systems of selfadjoint operators. By using the Cauchy integral formula available from Clifford analysis, the book examines how functions of a finite collection of operators can be formed when the Weyl calculus is not defined. The technique is applied to the determination of the support of the fundamental solution of a symmetric hyperbolic system of partial differential equations and to proving the boundedness of the Cauchy integral operator on a Lipschitz surface.
Author :D. Przeworska-Rolewicz Publisher :Springer Science & Business Media ISBN 13 :9401152128 Total Pages :367 pages Book Rating :4.4/5 (11 download)
Book Synopsis Logarithms and Antilogarithms by : D. Przeworska-Rolewicz
Download or read book Logarithms and Antilogarithms written by D. Przeworska-Rolewicz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume proposes and explores a new definition of logarithmic mappings as invertible selectors of multifunctions induced by linear operators with domains and ranges in an algebra over a field of characteristic zero. Several important previously published results are presented. Amongst the applications of logarithmic and antilogarithmic mappings are the solution of linear and nonlinear equations in algebras of square matrices. Some results may also provide numerical algorithms for the approximation of solutions. Audience: Research mathematicians and other scientists of other disciplines whose work involves the solution of equations.
Book Synopsis Mathematical Modelling of Heat and Mass Transfer Processes by : V.G. Danilov
Download or read book Mathematical Modelling of Heat and Mass Transfer Processes written by V.G. Danilov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present book the reader will find a review of methods for constructing a certain class of asymptotic solutions, which we call self-stabilizing solutions. This class includes solitons, kinks, traveling waves, etc. It can be said that either the solutions from this class or their derivatives are localized in the neighborhood of a certain curve or surface. For the present edition, the book published in Moscow by the Nauka publishing house in 1987, was almost completely revised, essentially up-dated, and shows our present understanding of the problems considered. The new results, obtained by the authors after the Russian edition was published, are referred to in footnotes. As before, the book can be divided into two parts: the methods for constructing asymptotic solutions ( Chapters I-V) and the application of these methods to some concrete problems (Chapters VI-VII). In Appendix a method for justification some asymptotic solutions is discussed briefly. The final formulas for the asymptotic solutions are given in the form of theorems. These theorems are unusual in form, since they present the results of calculations. The authors hope that the book will be useful to specialists both in differential equations and in the mathematical modeling of physical and chemical processes. The authors express their gratitude to Professor M. Hazewinkel for his attention to this work and his support.
Book Synopsis Banach Algebras and the General Theory of *-Algebras: Volume 2, *-Algebras by : Theodore W. Palmer
Download or read book Banach Algebras and the General Theory of *-Algebras: Volume 2, *-Algebras written by Theodore W. Palmer and published by Cambridge University Press. This book was released on 1994 with total page 846 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second of two volumes gives a modern exposition of the theory of Banach algebras.
Book Synopsis Recent Advances in Operator Theory, Operator Algebras, and their Applications by : Dumitru Gaspar
Download or read book Recent Advances in Operator Theory, Operator Algebras, and their Applications written by Dumitru Gaspar and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers peer-reviewed articles from the 19th International Conference on Operator Theory, Summer 2002. It contains recent developments in a broad range of topics from operator theory, operator algebras and their applications, particularly to differential analysis, complex functions, ergodic theory, mathematical physics, matrix analysis, and systems theory. The book covers a large variety of topics including single operator theory, C*-algebras, diffrential operators, integral transforms, stochastic processes and operators, and more.
Book Synopsis Boundary Value Problems in the Spaces of Distributions by : Y. Roitberg
Download or read book Boundary Value Problems in the Spaces of Distributions written by Y. Roitberg and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents elliptic, parabolic and hyperbolic boundary value problems for systems of mixed orders (Douglis-Nirenberg systems). For these problems the `theorem on complete collection of isomorphisms' is proven. Several applications in elasticity and hydrodynamics are treated. The book requires familiarity with the elements of functional analysis, the theory of partial differential equations, and the theory of generalized functions. Audience: This work will be of interest to graduate students and research mathematicians involved in areas such as functional analysis, partial differential equations, operator theory, the mathematics of mechanics, elasticity and viscoelasticity.
Book Synopsis Integration on Infinite-Dimensional Surfaces and Its Applications by : A. Uglanov
Download or read book Integration on Infinite-Dimensional Surfaces and Its Applications written by A. Uglanov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: It seems hard to believe, but mathematicians were not interested in integration problems on infinite-dimensional nonlinear structures up to 70s of our century. At least the author is not aware of any publication concerning this theme, although as early as 1967 L. Gross mentioned that the analysis on infinite dimensional manifolds is a field of research with rather rich opportunities in his classical work [2. This prediction was brilliantly confirmed afterwards, but we shall return to this later on. In those days the integration theory in infinite dimensional linear spaces was essentially developed in the heuristic works of RP. Feynman [1], I. M. Gelfand, A. M. Yaglom [1]). The articles of J. Eells [1], J. Eells and K. D. Elworthy [1], H. -H. Kuo [1], V. Goodman [1], where the contraction of a Gaussian measure on a hypersurface, in particular, was built and the divergence theorem (the Gauss-Ostrogradskii formula) was proved, appeared only in the beginning of the 70s. In this case a Gaussian specificity was essential and it was even pointed out in a later monograph of H. -H. Kuo [3] that the surface measure for the non-Gaussian case construction problem is not simple and has not yet been solved. A. V. Skorokhod [1] and the author [6,10] offered different approaches to such a construction. Some other approaches were offered later by Yu. L. Daletskii and B. D. Maryanin [1], O. G. Smolyanov [6], N. V.
Book Synopsis Lectures on Hyponormal Operators by : Mihai Putinar
Download or read book Lectures on Hyponormal Operators written by Mihai Putinar and published by Birkhäuser. This book was released on 2012-12-06 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present lectures are based on a course deli vered by the authors at the Uni versi ty of Bucharest, in the winter semester 1985-1986. Without aiming at completeness, the topics selected cover all the major questions concerning hyponormal operators. Our main purpose is to provide the reader with a straightforward access to an active field of research which is strongly related to the spectral and perturbation theories of Hilbert space operators, singular integral equations and scattering theory. We have in view an audience composed especially of experts in operator theory or integral equations, mathematical physicists and graduate students. The book is intended as a reference for the basic results on hyponormal operators, but has the structure of a textbook. Parts of it can also be used as a second year graduate course. As prerequisites the reader is supposed to be acquainted with the basic principles of functional analysis and operator theory as covered for instance by Reed and Simon [1]. A t several stages of preparation of the manuscript we were pleased to benefit from proper comments made by our cOlleagues: Grigore Arsene, Tiberiu Constantinescu, Raul Curto, Jan Janas, Bebe Prunaru, Florin Radulescu, Khrysztof Rudol, Konrad Schmudgen, Florian-Horia Vasilescu. We warmly thank them all. We are indebted to Professor Israel Gohberg, the editor of this series, for his constant encouragement and his valuable mathematical advice. We wish to thank Mr. Benno Zimmermann, the Mathematics Editor at Birkhauser Verlag, for cooperation and assistance during the preparation of the manuscript.
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 Scattering by Obstacles by : Alexander G. Ramm
Download or read book Scattering by Obstacles written by Alexander G. Ramm and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Book Synopsis Oscillation Theory of Two-Term Differential Equations by : Uri Elias
Download or read book Oscillation Theory of Two-Term Differential Equations written by Uri Elias and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Oscillation theory was born with Sturm's work in 1836. It has been flourishing for the past fifty years. Nowadays it is a full, self-contained discipline, turning more towards nonlinear and functional differential equations. Oscillation theory flows along two main streams. The first aims to study prop erties which are common to all linear differential equations. The other restricts its area of interest to certain families of equations and studies in maximal details phenomena which characterize only those equations. Among them we find third and fourth order equations, self adjoint equations, etc. Our work belongs to the second type and considers two term linear equations modeled after y(n) + p(x)y = O. More generally, we investigate LnY + p(x)y = 0, where Ln is a disconjugate operator and p(x) has a fixed sign. These equations enjoy a very rich structure and are the natural generalization of the Sturm-Liouville operator. Results about such equations are distributed over hundreds of research papers, many of them are reinvented again and again and the same phenomenon is frequently discussed from various points of view and different definitions of the authors. Our aim is to introduce an order into this plenty and arrange it in a unified and self contained way. The results are readapted and presented in a unified approach. In many cases completely new proofs are given and in no case is the original proof copied verbatim. Many new results are included.
Book Synopsis Convex and Starlike Mappings in Several Complex Variables by : Sheng Gong
Download or read book Convex and Starlike Mappings in Several Complex Variables written by Sheng Gong and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the theory of convex and starlike biholomorphic mappings in several complex variables. The underlying theme is the extension to several complex variables of geometric aspects of the classical theory of univalent functions. This is the first book which systematically studies this topic. It gathers together, and presents in a unified manner, the current state of affairs for convex and starlike biholomorphic mappings in several complex variables. The majority of the results presented are due to the author, his co-workers and his students. Audience: This volume will be of interest to research mathematicians whose work involves several complex variables and one complex variable.
Book Synopsis Geometry of CR-Submanifolds by : Aurel Bejancu
Download or read book Geometry of CR-Submanifolds written by Aurel Bejancu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can us;; Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Book Synopsis Trigonometric Fourier Series and Their Conjugates by : L. Zhizhiashvili
Download or read book Trigonometric Fourier Series and Their Conjugates written by L. Zhizhiashvili and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in the theory of trigonometric series has been carried out for over two centuries. The results obtained have greatly influenced various fields of mathematics, mechanics, and physics. Nowadays, the theory of simple trigonometric series has been developed fully enough (we will only mention the monographs by Zygmund [15, 16] and Bari [2]). The achievements in the theory of multiple trigonometric series look rather modest as compared to those in the one-dimensional case though multiple trigonometric series seem to be a natural, interesting and promising object of investigation. We should say, however, that the past few decades have seen a more intensive development of the theory in this field. To form an idea about the theory of multiple trigonometric series, the reader can refer to the surveys by Shapiro [1], Zhizhiashvili [16], [46], Golubov [1], D'yachenko [3]. As to monographs on this topic, only that ofYanushauskas [1] is known to me. This book covers several aspects of the theory of multiple trigonometric Fourier series: the existence and properties of the conjugates and Hilbert transforms of integrable functions; convergence (pointwise and in the LP-norm, p > 0) of Fourier series and their conjugates, as well as their summability by the Cesaro (C,a), a> -1, and Abel-Poisson methods; approximating properties of Cesaro means of Fourier series and their conjugates.
