Traces And Determinants Of Linear Operators
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Author |
: Israel Gohberg |
Publisher |
: Birkhäuser |
Total Pages |
: 261 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783034884013 |
ISBN-13 |
: 303488401X |
Rating |
: 4/5 (13 Downloads) |
Synopsis Traces and Determinants of Linear Operators by : Israel Gohberg
This 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 |
Total Pages |
: 224 |
Release |
: 2017-03-03 |
ISBN-10 |
: 9781498796910 |
ISBN-13 |
: 1498796915 |
Rating |
: 4/5 (10 Downloads) |
Synopsis Bounds for Determinants of Linear Operators and their Applications by : Michael Gil'
This 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 |
Total Pages |
: 877 |
Release |
: 2007-12-31 |
ISBN-10 |
: 9780817645960 |
ISBN-13 |
: 0817645969 |
Rating |
: 4/5 (60 Downloads) |
Synopsis History of Banach Spaces and Linear Operators by : Albrecht Pietsch
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.
Author |
: Themistocles M. Rassias |
Publisher |
: Springer |
Total Pages |
: 419 |
Release |
: 2019-05-31 |
ISBN-10 |
: 9783030126612 |
ISBN-13 |
: 3030126617 |
Rating |
: 4/5 (12 Downloads) |
Synopsis Analysis and Operator Theory by : Themistocles M. Rassias
Dedicated 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 |
Total Pages |
: 428 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783034879804 |
ISBN-13 |
: 3034879806 |
Rating |
: 4/5 (04 Downloads) |
Synopsis Basic Classes of Linear Operators by : Israel Gohberg
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.
Author |
: Daniel Alpay |
Publisher |
: Birkhäuser |
Total Pages |
: 396 |
Release |
: 2015-04-30 |
ISBN-10 |
: 9783319103358 |
ISBN-13 |
: 3319103350 |
Rating |
: 4/5 (58 Downloads) |
Synopsis Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes by : Daniel Alpay
The 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 |
Total Pages |
: 468 |
Release |
: 2012-12-19 |
ISBN-10 |
: 9783110262551 |
ISBN-13 |
: 311026255X |
Rating |
: 4/5 (51 Downloads) |
Synopsis Singular Traces by : Steven Lord
This 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 |
: Israel Gohberg |
Publisher |
: Birkhäuser |
Total Pages |
: 282 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783034881814 |
ISBN-13 |
: 3034881819 |
Rating |
: 4/5 (14 Downloads) |
Synopsis Linear Operators and Matrices by : Israel Gohberg
In September 1998, during the 'International Workshop on Analysis and Vibrat ing Systems' held in Canmore, Alberta, Canada, it was decided by a group of participants to honour Peter Lancaster on the occasion of his 70th birthday with a volume in the series 'Operator Theory: Advances and Applications'. Friends and colleagues responded enthusiastically to this proposal and within a short time we put together the volume which is now presented to the reader. Regarding accep tance of papers we followed the usual rules of the journal 'Integral Equations and Operator Theory'. The papers are dedicated to different problems in matrix and operator theory, especially to the areas in which Peter contributed so richly. At our request, Peter agreed to write an autobiographical paper, which appears at the beginning of the volume. It continues with the list of Peter's publications. We believe that this volume will pay tribute to Peter on his outstanding achievements in different areas of mathematics. 1. Gohberg, H. Langer P ter Lancast r *1929 Operator Theory: Advances and Applications, Vol. 130, 1- 7 © 2001 Birkhiiuser Verlag Basel/Switzerland My Life and Mathematics Peter Lancaster I was born in Appleby, a small county town in the north of England, on November 14th, 1929. I had two older brothers and was to have one younger sister. My family moved around the north of England as my father's work in an insurance company required.
Author |
: Tosio Kato |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 610 |
Release |
: 2013-06-29 |
ISBN-10 |
: 9783662126783 |
ISBN-13 |
: 3662126788 |
Rating |
: 4/5 (83 Downloads) |
Synopsis Perturbation theory for linear operators by : Tosio Kato
Author |
: Steven Lord |
Publisher |
: Walter de Gruyter GmbH & Co KG |
Total Pages |
: 416 |
Release |
: 2021-07-19 |
ISBN-10 |
: 9783110378054 |
ISBN-13 |
: 3110378051 |
Rating |
: 4/5 (54 Downloads) |
Synopsis Theory by : Steven Lord
This 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.