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Author: Israel Gohberg
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 261
ISBN-13: 303488401X
DOWNLOAD EBOOKThis book is dedicated to a theory of traces and determinants on embedded algebras of linear operators, where the trace and determinant are extended from finite rank operators by a limit process. The self-contained material should appeal to a wide group of mathematicians and engineers, and is suitable for teaching.
Author: Michael Gil'
Publisher: CRC Press
Published: 2017-03-03
Total Pages: 224
ISBN-13: 1498796915
DOWNLOAD EBOOKThis book deals with the determinants of linear operators in Euclidean, Hilbert and Banach spaces. Determinants of operators give us an important tool for solving linear equations and invertibility conditions for linear operators, enable us to describe the spectra, to evaluate the multiplicities of eigenvalues, etc. We derive upper and lower bounds, and perturbation results for determinants, and discuss applications of our theoretical results to spectrum perturbations, matrix equations, two parameter eigenvalue problems, as well as to differential, difference and functional-differential equations.
Author: Albrecht Pietsch
Publisher: Springer Science & Business Media
Published: 2007-12-31
Total Pages: 877
ISBN-13: 0817645969
DOWNLOAD EBOOKWritten 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.
Author: Themistocles M. Rassias
Publisher: Springer
Published: 2019-05-31
Total Pages: 416
ISBN-13: 3030126617
DOWNLOAD EBOOKDedicated to Tosio Kato’s 100th birthday, this book contains research and survey papers on a broad spectrum of methods, theories, and problems in mathematics and mathematical physics. Survey papers and in-depth technical papers emphasize linear and nonlinear analysis, operator theory, partial differential equations, and functional analysis including nonlinear evolution equations, the Korteweg–de Vries equation, the Navier–Stokes equation, and perturbation theory of linear operators. The Kato inequality, the Kato type matrix limit theorem, the Howland–Kato commutator problem, the Kato-class of potentials, and the Trotter–Kato product formulae are discussed and analyzed. Graduate students, research mathematicians, and applied scientists will find that this book provides comprehensive insight into the significance of Tosio Kato’s impact to research in analysis and operator theory.
Author: Israel Gohberg
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 428
ISBN-13: 3034879806
DOWNLOAD EBOOKA 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.
Author: Daniel Alpay
Publisher: Birkhäuser
Published: 2015-04-30
Total Pages: 396
ISBN-13: 3319103350
DOWNLOAD EBOOKThe volume is dedicated to Lev Sakhnovich, who made fundamental contributions in operator theory and related topics. Besides bibliographic material, it includes a number of selected papers related to Lev Sakhnovich's research interests. The papers are related to operator identities, moment problems, random matrices and linear stochastic systems.
Author: Steven Lord
Publisher: Walter de Gruyter
Published: 2012-12-19
Total Pages: 468
ISBN-13: 311026255X
DOWNLOAD EBOOKThis book is the first complete study and monograph dedicated to singular traces. The text mathematically formalises the study of traces in a self contained theory of functional analysis. Extensive notes will treat the historical development. The final section will contain the most complete and concise treatment known of the integration half of Connes' quantum calculus. Singular traces are traces on ideals of compact operators that vanish on the subideal of finite rank operators. Singular traces feature in A. Connes' interpretation of noncommutative residues. Particularly the Dixmier trace,which generalises the restricted Adler-Manin-Wodzicki residue of pseudo-differential operators and plays the role of the residue for a new catalogue of 'geometric' spaces, including Connes-Chamseddine standard models, Yang-Mills action for quantum differential forms, fractals, isospectral deformations, foliations and noncommutative index theory. The theory of singular traces has been studied after Connes' application to non-commutative geometry and physics by various authors. Recent work by Nigel Kalton and the authors has advanced the theory of singular traces.Singular traces can be equated to symmetric functionals of symmetric sequence or function spaces, residues of zeta functions and heat kernel asymptotics, and characterised by Lidksii and Fredholm formulas. The traces and formulas used in noncommutative geometry are now completely understood in this theory, with surprising new mathematical and physical consequences. For mathematical readers the text offers fundamental functional analysis results and, due to Nigel Kalton's contribution, a now complete theory of traces on compact operators. For mathematical physicists and other users of Connes' noncommutative geometry the text offers a complete reference to Dixmier traces and access to the deeper mathematical features of traces on ideals associated to the harmonic sequence. These features, not known and not discussed in general texts on noncommutative geometry, are undoubtably physical and probe to the fascinating heart of classical limits and quantization.
Author: Steven Lord
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2021-07-19
Total Pages: 416
ISBN-13: 3110378051
DOWNLOAD EBOOKThis book is the second edition of the first complete study and monograph dedicated to singular traces. The text offers, due to the contributions of Albrecht Pietsch and Nigel Kalton, a complete theory of traces and their spectral properties on ideals of compact operators on a separable Hilbert space. The second edition has been updated on the fundamental approach provided by Albrecht Pietsch. For mathematical physicists and other users of Connes’ noncommutative geometry the text offers a complete reference to traces on weak trace class operators, including Dixmier traces and associated formulas involving residues of spectral zeta functions and asymptotics of partition functions.
Author: Nihon Sūgakkai
Publisher: MIT Press
Published: 1993
Total Pages: 1180
ISBN-13: 9780262590204
DOWNLOAD EBOOKV.1. A.N. v.2. O.Z. Apendices and indexes.
Author: M.-W. Wong
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 164
ISBN-13: 3034882173
DOWNLOAD EBOOKThis book is based on lectures given at the Global Analysis Research Center (GARC) of Seoul National University in 1999and at Peking University in 1999and 2000. Preliminary versions of the book have been used for various topics courses in analysis for graduate students at York University. We study in this book wavelet transforms and localization operators in the context of infinite-dimensional and square-integrable representations of locally compact and Hausdorffgroups. The wavelet transforms studied in this book, which include the ones that come from the Weyl-Heisenberg group and the well-known affine group, are the building blocks of localization operators. The theme that dominates the book is the spectral theory of wavelet transforms and localization operators in the form of Schatten-von Neumann norm inequalities. Several chap ters are also devoted to the product formulas for concrete localization operators such as Daubechies operators and wavelet multipliers. This book is a natural sequel to the book on pseudo-differential operators [103] and the book on Weyl transforms [102] by the author. Indeed, localization operators on the Weyl-Heisenberg group are Weyl transforms, which are in fact pseudo-differential operators. Details on the perspective and the organization of the book are laid out in the first chapter. This is a book on mathematics and is written for anyone who has taken basic graduate courses in measure theory and functional analysis. Some knowledge of group theory and general topology at the undergraduate level is also assumed.
