Holomorphic Functions and Integral Representations in Several Complex Variables


Author: R. Michael Range

Publisher: Springer Science & Business Media

ISBN: 1475719183

Category: Mathematics

Page: 392

View: 9974

The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains inC", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particu lar, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differ ential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between com plex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods.

Topics in Operator Theory

Volume 1: Operators, Matrices and Analytic functions


Author: Joseph A. Ball,Vladimir Bolotnikov,J. William Helton,Leiba Rodman,Ilya M. Spitkovsky

Publisher: Springer Science & Business Media

ISBN: 9783034601580

Category: Mathematics

Page: 600

View: 4952

This is the first volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.

First Steps in Several Complex Variables

Reinhardt Domains


Author: Marek Jarnicki,Peter Pflug

Publisher: European Mathematical Society

ISBN: 9783037190494

Category: Functions of several complex variables

Page: 359

View: 8167

Operator Theory, Operator Algebras, and Matrix Theory


Author: Carlos André,M. Amélia Bastos,Alexei Yu. Karlovich,Bernd Silbermann,Ion Zaballa

Publisher: Birkhäuser

ISBN: 3319724495

Category: Mathematics

Page: 372

View: 1089

This book consists of invited survey articles and research papers in the scientific areas of the “International Workshop on Operator Algebras, Operator Theory and Applications,” which was held in Lisbon in July 2016. Reflecting recent developments in the field of algebras of operators, operator theory and matrix theory, it particularly focuses on groupoid algebras and Fredholm conditions, algebras of approximation sequences, C* algebras of convolution type operators, index theorems, spectrum and numerical range of operators, extreme supercharacters of infinite groups, quantum dynamics and operator algebras, and inverse eigenvalue problems. Establishing bridges between the three related areas of operator algebras, operator theory, and matrix theory, the book is aimed at researchers and graduate students who use results from these areas.

Banach Algebras 97

Proceedings of the 13th International Conference on Banach Algebras held at the Heinrich Fabri Institute of the University of Tübingen in Blaubeuren, July 20-August 3, 1997


Author: Ernst Albrecht,Martin Mathieu

Publisher: Walter de Gruyter

ISBN: 3110802007

Category: Mathematics

Page: 575

View: 2309

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Introduction to Banach Spaces and Algebras


Author: Graham R. Allan,Harold G. Dales

Publisher: Oxford University Press

ISBN: 0199206538

Category: Banach algebras

Page: 371

View: 1767

A graduate level text in functional analysis, with an emphasis on Banach algebras. Based on lectures given for Part III of the Cambridge Mathematical Tripos, the text will assume a familiarity with elementary real and complex analysis, and some acquaintance with metric spaces, analytic topology and normed spaces (but not theorems depending on Baire category, or any version of the Hahn-Banach theorem).

CMA/AMSI Research Symposium "Asymptotic Geometric Analysis, Harmonic Analysis, and Related Topics"

Murramarang, NSW, 21-24 February 2006


Author: Australian National University. Centre for Mathematics and Its Applications,Australian Mathematical Sciences Institute

Publisher: N.A


Category: Differential geometry

Page: 135

View: 6867