Toeplitz Operators And Index Theory In Several Complex Variables

Author : Harald Upmeier
Publisher : Birkhäuser
Page : 495 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034892469

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Toeplitz Operators and Index Theory in Several Complex Variables by Harald Upmeier Pdf

4. 1 Bergman-Toeplitz Operators Over Bounded Domains 242 4. 2 Hardy-Toeplitz Operators Over Strictly Domains Pseudoconvex 250 Groupoid C* -Algebras 4. 3 256 4. 4 Hardy-Toeplitz Operators Over Tubular Domains 267 4. 5 Bergman-Toeplitz Operators Over Tubular Domains 278 4. 6 Hardy-Toeplitz Operators Over Polycircular Domains 284 4. 7 Bergman-Toeplitz Operators Over Polycircular Domains 290 4. 8 Hopf C* -Algebras 299 4. 9 Actions and Coactions on C* -Algebras 310 4. 10 Hardy-Toeplitz Operators Over K-circular Domains 316 4. 11 Hardy-Toeplitz Operators Over Symmetric Domains 325 4. 12 Bergman-Toeplitz Operators Over Symmetric Domains 361 5. Index Theory for Multivariable Toeplitz Operators 5. 0 Introduction 371 5. 1 K-Theory for Topological Spaces 372 5. 2 Index Theory for Strictly Pseudoconvex Domains 384 5. 3 C*-Algebras K-Theory for 394 5. 4 Index Theory for Symmetric Domains 400 5. 5 Index Theory for Tubular Domains 432 5. 6 Index Theory for Polycircular Domains 455 References 462 Index of Symbols and Notations 471 In trod uction Toeplitz operators on the classical Hardy space (on the I-torus) and the closely related Wiener-Hopf operators (on the half-line) form a central part of operator theory, with many applications e. g. , to function theory on the unit disk and to the theory of integral equations.

Author : Vladimir Dybin,Sergei M. Grudsky
Publisher : Birkhäuser
Page : 306 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882132

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Introduction to the Theory of Toeplitz Operators with Infinite Index by Vladimir Dybin,Sergei M. Grudsky Pdf

This book is devoted to Toeplitz and singular integral operators with symbols that have discontinuities of the oscillating type. Criteria for the normal solvability of such operators are established and several methods for describing the kernel and image spaces of the operators are presented. The approach is based on the idea of modelling discontinuities with an "infinite index" by appropriate inner functions, especially by infinite Blaschke products. The corresponding techniques have been elaborated by the authors during the last two decades, and they are applicable to both symbols with slowly and rapidly increasing arguments. Moreover, the book reveals exciting connections between invariant subspaces of the shift operator, bases in Banach spaces, and various classes of entire and meromorphic functions. The book aims at making advanced topics accessible to a broad readership. It is addressed to graduate and postgraduate students and to mathematicians interested in functional analysis, the theory of functions of a complex variable, or mathematical physics.

Author : Kehe Zhu
Publisher : CRC Press
Page : 228 pages
File Size : 51,9 Mb
Release : 2019-05-10
Category : Mathematics
ISBN : 9781351045537

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Handbook of Analytic Operator Theory by Kehe Zhu Pdf

This handbook concerns the subject of holomorphic function spaces and operators acting on them. Topics include Bergman spaces, Hardy spaces, Besov/Sobolev spaces, Fock spaces, and the space of Dirichlet series. Operators discussed in the book include Toeplitz operators, Hankel operators, composition operators, and Cowen-Douglas class operators

Author : Marek Ptak
Publisher : Springer Nature
Page : 423 pages
File Size : 52,6 Mb
Release : 2024-06-02
Category : Electronic
ISBN : 9783031506130

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Operator and Matrix Theory, Function Spaces, and Applications by Marek Ptak Pdf

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 564 pages
File Size : 48,8 Mb
Release : 2007-11-23
Category : Mathematics
ISBN : 9780306483738

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Encyclopaedia of Mathematics, Supplement III by Michiel Hazewinkel Pdf

This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Author : Victor W. Guillemin,Johannes Sjöstrand
Publisher : Birkhäuser
Page : 852 pages
File Size : 53,5 Mb
Release : 2017-05-05
Category : Mathematics
ISBN : 9783319279091

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Louis Boutet de Monvel, Selected Works by Victor W. Guillemin,Johannes Sjöstrand Pdf

This book features a selection of articles by Louis Boutet de Monvel and presents his contributions to the theory of partial differential equations and analysis. The works selected here reveal his central role in the development of his field, including three cornerstones: firstly, analytic pseudodifferential operators, which have become a fundamental aspect of analytic microlocal analysis, and secondly the Boutet de Monvel calculus for boundary problems for elliptic partial differential operators, which is still an important tool also in index theory. Thirdly, Boutet de Monvel was one of the first people to recognize the importance of the existence of generalized functions, whose singularities are concentrated on a single ray in phase space, which led him to make essential contributions to hypoelliptic operators and to a very successful and influential calculus of Toeplitz operators with applications to spectral and index theory. Other topics treated here include microlocal analysis, star products and deformation quantization as well as problems in several complex variables, index theory and geometric quantization. This book will appeal to both experts in the field and students who are new to this subject.

Author : Léa Blanc-Centi
Publisher : Springer
Page : 173 pages
File Size : 44,6 Mb
Release : 2017-11-03
Category : Mathematics
ISBN : 9783319658377

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Metrical and Dynamical Aspects in Complex Analysis by Léa Blanc-Centi Pdf

The central theme of this reference book is the metric geometry of complex analysis in several variables. Bridging a gap in the current literature, the text focuses on the fine behavior of the Kobayashi metric of complex manifolds and its relationships to dynamical systems, hyperbolicity in the sense of Gromov and operator theory, all very active areas of research. The modern points of view expressed in these notes, collected here for the first time, will be of interest to academics working in the fields of several complex variables and metric geometry. The different topics are treated coherently and include expository presentations of the relevant tools, techniques and objects, which will be particularly useful for graduate and PhD students specializing in the area.

Author : Uwe Kähler,Michael Reissig,Irene Sabadini,Jasson Vindas
Publisher : Springer Nature
Page : 696 pages
File Size : 47,5 Mb
Release : 2023-12-01
Category : Mathematics
ISBN : 9783031363757

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Analysis, Applications, and Computations by Uwe Kähler,Michael Reissig,Irene Sabadini,Jasson Vindas Pdf

This volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium. The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.

Author : Peter B. Gilkey
Publisher : CRC Press
Page : 536 pages
File Size : 42,5 Mb
Release : 2018-05-02
Category : Mathematics
ISBN : 9781351436434

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Invariance Theory by Peter B. Gilkey Pdf

This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a manifold with smooth boundary. The author uses invariance theory to identify the integrand of the index theorem for classical elliptic complexes with the invariants of the heat equation.

Author : Raul E Curto,William Helton,Huaxin Lin,Xiang Tang,Rongwei Yang,Guoliang Yu
Publisher : Springer Nature
Page : 531 pages
File Size : 50,7 Mb
Release : 2020-12-12
Category : Mathematics
ISBN : 9783030433802

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Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology by Raul E Curto,William Helton,Huaxin Lin,Xiang Tang,Rongwei Yang,Guoliang Yu Pdf

This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology. Its goal is to give graduate students and researchers a relatively comprehensive overview of the current status of research in the relevant fields. The book is also a special volume dedicated to the memory of Ronald G. Douglas who passed away on February 27, 2018 at the age of 79. Many of the contributors are Douglas’ students and past collaborators. Their articles attest and commemorate his life-long contribution and influence to these fields.

Author : Kehe Zhu
Publisher : American Mathematical Soc.
Page : 368 pages
File Size : 41,6 Mb
Release : 2007
Category : Function spaces
ISBN : 9780821839652

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Operator Theory in Function Spaces by Kehe Zhu Pdf

This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.

Author : Farhad Jafari,Rocky Mountain Mathematics Consortium
Publisher : American Mathematical Soc.
Page : 252 pages
File Size : 43,8 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821807682

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Studies on Composition Operators by Farhad Jafari,Rocky Mountain Mathematics Consortium Pdf

This book reflects the proceedings of the 1996 Rocky Mountain Mathematics Consortium conference on ``Composition Operators on Spaces of Analytic Functions'' held at the University of Wyoming. The readers will find here a collection of high-quality research and expository articles on composition operators in one and several variables. The book highlights open questions and new advances in the classical areas and promotes topics which are left largely untreated in the existing texts. In the past two decades, the study of composition operators has experienced tremendous growth. Many connections between the study of these operators on various function spaces and other branches of analysis have been established. Advances in establishing criteria for membership in different operator classes have led to progress in the study of the spectra, adjoints, and iterates of these operators. More recently, connections between these operators and the study of the invariant subspace problem, functional equations, and dynamical systems have been exploited.

Author : Eric Bedford
Publisher : American Mathematical Soc.
Page : 368 pages
File Size : 46,6 Mb
Release : 1991
Category : Mathematics
ISBN : 9780821814918

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Several Complex Variables and Complex Geometry, Part III by Eric Bedford Pdf

Author : Stephan Rempel,Bert-Wolfgang Schulze
Publisher : Walter de Gruyter GmbH & Co KG
Page : 396 pages
File Size : 43,5 Mb
Release : 1982-12-31
Category : Mathematics
ISBN : 9783112707159

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Index Theory of Elliptic Boundary Problems by Stephan Rempel,Bert-Wolfgang Schulze Pdf

No detailed description available for "Index Theory of Elliptic Boundary Problems".

Author : Nigel Higson,John Roe
Publisher : OUP Oxford
Page : 426 pages
File Size : 43,7 Mb
Release : 2000-12-07
Category : Mathematics
ISBN : 9780191589201

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Analytic K-Homology by Nigel Higson,John Roe Pdf

Analytic K-homology draws together ideas from algebraic topology, functional analysis and geometry. It is a tool - a means of conveying information among these three subjects - and it has been used with specacular success to discover remarkable theorems across a wide span of mathematics. The purpose of this book is to acquaint the reader with the essential ideas of analytic K-homology and develop some of its applications. It includes a detailed introduction to the necessary functional analysis, followed by an exploration of the connections between K-homology and operator theory, coarse geometry, index theory, and assembly maps, including a detailed treatment of the Atiyah-Singer Index Theorem. Beginning with the rudiments of C* - algebra theory, the book will lead the reader to some central notions of contemporary research in geometric functional analysis. Much of the material included here has never previously appeared in book form.