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Analytic Hilbert Modules
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Book Synopsis Analytic Hilbert Modules by : Xiaoman Chen
Download or read book Analytic Hilbert Modules written by Xiaoman Chen and published by CRC Press. This book was released on 2003-03-26 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The seminal 1989 work of Douglas and Paulsen on the theory of analytic Hilbert modules precipitated a number of major research efforts. This in turn led to some intriguing and valuable results, particularly in the areas of operator theory and functional analysis. With the field now beginning to blossom, the time has come to collect those results un
Book Synopsis Handbook of Analytic Operator Theory by : Kehe Zhu
Download or read book Handbook of Analytic Operator Theory written by Kehe Zhu and published by CRC Press. This book was released on 2019-05-10 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Hilbert Functions of Filtered Modules by : Maria Evelina Rossi
Download or read book Hilbert Functions of Filtered Modules written by Maria Evelina Rossi and published by Springer Science & Business Media. This book was released on 2010-08-25 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert Functions play major roles in Algebraic Geometry and Commutative Algebra, and are becoming increasingly important also in Computational Algebra. They capture many useful numerical characters associated to a projective variety or to a filtered module over a local ring. Starting from the pioneering work of D.G. Northcott and J. Sally, we aim to gather together in one place many new developments of this theory by using a unifying approach which gives self-contained and easier proofs. The extension of the theory to the case of general filtrations on a module, and its application to the study of certain graded algebras which are not associated to a filtration are two of the main features of the monograph. The material is intended for graduate students and researchers who are interested in Commutative Algebra, in particular in the theory of the Hilbert Functions and related topics.
Book Synopsis Multivariable Operator Theory by : Ernst Albrecht
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.
Book Synopsis Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology by : Raul E Curto
Download or read book Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology written by Raul E Curto and published by Springer Nature. This book was released on 2020-12-12 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Hilbert Modular Surfaces by : Gerard van der Geer
Download or read book Hilbert Modular Surfaces written by Gerard van der Geer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last 15 years important results have been achieved in the field of Hilbert Modular Varieties. Though the main emphasis of this book is on the geometry of Hilbert modular surfaces, both geometric and arithmetic aspects are treated. An abundance of examples - in fact a whole chapter - completes this competent presentation of the subject. This Ergebnisbericht will soon become an indispensible tool for graduate students and researchers in this field.
Book Synopsis Hilbert C*-modules by : Vladimir Markovich Manuĭlov
Download or read book Hilbert C*-modules written by Vladimir Markovich Manuĭlov and published by American Mathematical Soc.. This book was released on with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on lectures delivered by the authors at Moscow State University, this volume presents a detailed introduction to the theory of Hilbert $C*$-modules. Hilbert $C*$-modules provide a natural generalization of Hilbert spaces arising when the field of scalars $\mathbf{C $ is replaced by an arbitrary $C*$-algebra. The general theory of Hilbert $C*$-modules appeared more than 30 years ago in the pioneering papers of W. Paschke and M. Rieffel and has proved to be a powerful tool inoperator algebras theory, index theory of elliptic operators, $K$- and $KK$-theory, and in noncommutative geometry as a whole. Alongside these applications, the theory of Hilbert $C*$-modules is interesting on its own. In this book, the authors explain in detail the basic notions and results of thetheory, and provide a number of important examples. Some results related to the authors' research interests are also included. A large part of the book is devoted to structural results (self-duality, reflexivity) and to nonadjointable operators. Most of the book can be read with only a basic knowledge of functional analysis; however, some experience in the theory of operator algebras makes reading easier.
Book Synopsis Lectures on Analytic Function Spaces and their Applications by : Javad Mashreghi
Download or read book Lectures on Analytic Function Spaces and their Applications written by Javad Mashreghi and published by Springer Nature. This book was released on 2023-11-14 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert spaces of analytic functions form one of the pillars of complex analysis. These spaces have a rich structure and for more than a century have been studied by many prominent mathematicians. They have essential applications in other fields of mathematics and engineering. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins—the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b)—have also garnered attention in recent decades. Leading experts on function spaces gathered and discussed new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains. With over 250 hours of lectures by prominent mathematicians, the program spanned a wide variety of topics. More explicitly, there were courses and workshops on Interpolation and Sampling, Riesz Bases, Frames and Signal Processing, Bounded Mean Oscillation, de Branges-Rovnyak Spaces, Blaschke Products and Inner Functions, and Convergence of Scattering Data and Non-linear Fourier Transform, among others. At the end of each week, there was a high-profile colloquium talk on the current topic. The program also contained two advanced courses on Schramm Loewner Evolution and Lattice Models and Reproducing Kernel Hilbert Space of Analytic Functions. This volume features the courses given on Hardy Spaces, Dirichlet Spaces, Bergman Spaces, Model Spaces, Operators on Function Spaces, Truncated Toeplitz Operators, Semigroups of weighted composition operators on spaces of holomorphic functions, the Corona Problem, Non-commutative Function Theory, and Drury-Arveson Space. This volume is a valuable resource for researchers interested in analytic function spaces.
Book Synopsis Multiplication Operators on the Bergman Space by : Kunyu Guo
Download or read book Multiplication Operators on the Bergman Space written by Kunyu Guo and published by Springer. This book was released on 2015-06-23 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with various aspects of commutants and reducing subspaces of multiplication operators on the Bergman space, along with relevant von Neumann algebras generated by these operators, which have been the focus of considerable attention from the authors and other experts in recent years. The book reviews past developments and offers insights into cutting-edge developments in the study of multiplication operators. It also provides commentary and comparisons to stimulate research in this area.
Book Synopsis D-Modules, Perverse Sheaves, and Representation Theory by : Ryoshi Hotta
Download or read book D-Modules, Perverse Sheaves, and Representation Theory written by Ryoshi Hotta and published by Springer Science & Business Media. This book was released on 2007-11-07 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.
Book Synopsis Dictionary of Analysis, Calculus, and Differential Equations by : Douglas N. Clark
Download or read book Dictionary of Analysis, Calculus, and Differential Equations written by Douglas N. Clark and published by CRC Press. This book was released on 1999-12-15 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clear, rigorous definitions of mathematical terms are crucial to good scientific and technical writing-and to understanding the writings of others. Scientists, engineers, mathematicians, economists, technical writers, computer programmers, along with teachers, professors, and students, all have the occasional-if not frequent-need for comprehensible, working definitions of mathematical expressions. To meet that need, CRC Press proudly introduces its Dictionary of Analysis, Calculus, and Differential Equations - the first published volume in the CRC Comprehensive Dictionary of Mathematics. More than three years in development, top academics and professionals from prestigious institutions around the world bring you more than 2,500 detailed definitions, written in a clear, readable style and complete with alternative meanings, and related references.
Book Synopsis Spectral Analysis of Quantum Hamiltonians by : Rafael Benguria
Download or read book Spectral Analysis of Quantum Hamiltonians written by Rafael Benguria and published by Springer Science & Business Media. This book was released on 2012-06-30 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains surveys as well as research articles broadly centered on spectral analysis. Topics range from spectral continuity for magnetic and pseudodifferential operators to localization in random media, from the stability of matter to properties of Aharonov-Bohm and Quantum Hall Hamiltonians, from waveguides and resonances to supersymmetric models and dissipative fermion systems. This is the first of a series of volumes reporting every two years on recent progress in spectral theory.
Book Synopsis Hilbert C*-Modules by : E. Christopher Lance
Download or read book Hilbert C*-Modules written by E. Christopher Lance and published by Cambridge University Press. This book was released on 1995-03-16 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert C*-modules are objects like Hilbert spaces, except that the inner product, instead of being complex valued, takes its values in a C*-algebra. The theory of these modules, together with their bounded and unbounded operators, is not only rich and attractive in its own right but forms an infrastructure for some of the most important research topics in operator algebras. This book is based on a series of lectures given by Professor Lance at a summer school at the University of Trondheim. It provides, for the first time, a clear and unified exposition of the main techniques and results in this area, including a substantial amount of new and unpublished material. It will be welcomed as an excellent resource for all graduate students and researchers working in operator algebras.
Book Synopsis Integral Closure of Ideals, Rings, and Modules by : Craig Huneke
Download or read book Integral Closure of Ideals, Rings, and Modules written by Craig Huneke and published by Cambridge University Press. This book was released on 2006-10-12 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Book Synopsis Commutative and Noncommutative Harmonic Analysis and Applications by : Azita Mayeli
Download or read book Commutative and Noncommutative Harmonic Analysis and Applications written by Azita Mayeli and published by American Mathematical Soc.. This book was released on 2013-11-08 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Wavelet and Frame Theoretic Methods in Harmonic Analysis and Partial Differential Equations, held September 22-23, 2012, at the Rochester Institute of Technology, Rochester, NY, USA. The book features new directions, results and ideas in commutative and noncommutative abstract harmonic analysis, operator theory and applications. The commutative part includes shift invariant spaces, abelian group action on Euclidean space and frame theory; the noncommutative part includes representation theory, continuous and discrete wavelets related to four dimensional Euclidean space, frames on symmetric spaces, $C DEGREES*$-algebras, projective multiresolutions, and free probability algebras. The scope of the book goes beyond traditional harmonic analysis, dealing with Fourier tools, transforms, Fourier bases, and associated function spaces. A number of papers take the step toward wavelet analysis, and even more general tools for analysis/synthesis problems, including papers on frames (over-complete bases) and their practical applications to engineering, cosmology and astrophysics.Other applications in this book include explicit families of wavelets and frames, as they are used in signal processing, multiplexing, and the study of Cosmic Microwave Background (CMB) radiation. For the purpose of organisation, the book is divided into three parts: noncommutative, commutative, and applications. The first group of papers are devoted to problems in noncommutative harmonic analysis, the second to topics in commutative harmonic analysis, and the third to such applications as wavelet and frame theory and to some real-world applications.
Book Synopsis Analysis, Geometry and Topology of Elliptic Operators by : Bernhelm Booss
Download or read book Analysis, Geometry and Topology of Elliptic Operators written by Bernhelm Booss and published by World Scientific. This book was released on 2006 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern theory of elliptic operators, or simply elliptic theory, has been shaped by the Atiyah-Singer Index Theorem created 40 years ago. Reviewing elliptic theory over a broad range, 32 leading scientists from 14 different countries present recent developments in topology; heat kernel techniques; spectral invariants and cutting and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics.The first of its kind, this volume is ideally suited to graduate students and researchers interested in careful expositions of newly-evolved achievements and perspectives in elliptic theory. The contributions are based on lectures presented at a workshop acknowledging Krzysztof P Wojciechowski's work in the theory of elliptic operators.
Book Synopsis The Madison Symposium on Complex Analysis by : Edgar Lee Stout
Download or read book The Madison Symposium on Complex Analysis written by Edgar Lee Stout and published by American Mathematical Soc.. This book was released on 1992 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of a Symposium on Complex Analysis, held at the University of Wisconsin at Madison in June 1991 on the occasion of the retirement of Walter Rudin. During the week of the conference, a group of about two hundred mathematicians from many nations gathered to discuss recent developments in complex analysis and to celebrate Rudin's long and productive career. Among the main subjects covered are applications of complex analysis to operator theory, polynomial convexity, holomorphic mappings, boundary behaviour of holomorphic functions, function theory on the unit disk and ball, and some aspects of the theory of partial differential equations related to complex analysis. Containing papers by some of the world's leading experts in these subjects, this book reports on current directions in complex analysis and presents an excellent mixture of the analytic and geometric aspects of the theory.
