Several Complex Variables And Banach Algebras
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Banach Algebras And Several Complex Variables
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Author : John Wermer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Banach Algebras And Several Complex Variables written by John Wermer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
During the past twenty years many connections have been found between the theory of analytic functions of one or more complex variables and the study of commutative Banach algebras. On the one hand, function theory has been used to answer algebraic questions such as the question of the existence of idempotents in a Banach algebra. On the other hand, concepts arising from the study of Banach algebras such as the maximal ideal space, the Silov boundary, Gleason parts, etc. have led to new questions and to new methods of proof in function theory. Roughly one third of this book isconcerned with developing some of the principal applications of function theory in several complex variables to Banach algebras. We presuppose no knowledge of severalcomplex variables on the part of the reader but develop the necessary material from scratch. The remainder of the book deals with problems of uniform approximation on compact subsets of the space of n complex variables. For n > I no complete theory exists but many important particular problems have been solved. Throughout, our aim has been to make the exposition elementary and self-contained. We have cheerfully sacrificed generality and completeness all along the way in order to make it easier to understand the main ideas.
Several Complex Variables And Banach Algebras
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Author : Herbert Alexander
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-17
Several Complex Variables And Banach Algebras written by Herbert Alexander and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-17 with Mathematics categories.
Many connections have been found between the theory of analytic functions of one or more complex variables and the study of commutative Banach algebras. While function theory has often been employed to answer algebraic questions such as the existence of idempotents in a Banach algebra, concepts arising from the study of Banach algebras including the maximal ideal space, the Silov boundary, Geason parts, etc. have led to new questions and to new methods of proofs in function theory. This book is concerned with developing some of the principal applications of function theory in several complex variables to Banach algebras. The authors do not presuppose any knowledge of several complex variables on the part of the reader and all relevant material is developed within the text. Furthermore, the book deals with problems of uniform approximation on compact subsets of the space of n complex variables. The third edition of this book contains new material on; maximum modulus algebras and subharmonicity, the hull of a smooth curve, integral kernels, perturbations of the Stone-Weierstrass Theorem, boundaries of analytic varieties, polynomial hulls of sets over the circle, areas, and the topology of hulls. The authors have also included a new chapter containing commentaries on history and recent developments and an updated and expanded reading list.
Several Complex Variables And Banach Algebras
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Author : Herbert Alexander
language : en
Publisher:
Release Date : 2014-01-15
Several Complex Variables And Banach Algebras written by Herbert Alexander and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Proceedings Of The Conference On Banach Algebras And Several Complex Variables
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Author : Frederick P. Greenleaf
language : en
Publisher: American Mathematical Soc.
Release Date : 1984
Proceedings Of The Conference On Banach Algebras And Several Complex Variables written by Frederick P. Greenleaf and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Contains papers presented at the conference on Banach Algebras and Several Complex Variables held June 21-24, 1983, to honor Professor Charles E Rickart upon his retirement from Yale University. This work includes articles that present advances in topics related to Banach algebras, function algebras and infinite dimensional holomorphy.
Applications Of The Theory Of Several Complex Variables To Banach Algebras
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Author : Joan M. Negrepontis
language : en
Publisher:
Release Date : 1967
Applications Of The Theory Of Several Complex Variables To Banach Algebras written by Joan M. Negrepontis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Banach spaces categories.
Several Complex Variables With Connections To Algebraic Geometry And Lie Groups
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Author : Joseph L. Taylor
language : en
Publisher: American Mathematical Society
Release Date : 2025-03-21
Several Complex Variables With Connections To Algebraic Geometry And Lie Groups written by Joseph L. Taylor and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-21 with Mathematics categories.
This text presents an integrated development of the theory of several complex variables and complex algebraic geometry, leading to proofs of Serre's celebrated GAGA theorems relating the two subjects, and including applications to the representation theory of complex semisimple Lie groups. It includes a thorough treatment of the local theory using the tools of commutative algebra, an extensive development of sheaf theory and the theory of coherent analytic and algebraic sheaves, proofs of the main vanishing theorems for these categories of sheaves, and a complete proof of the finite dimensionality of the cohomology of coherent sheaves on compact varieties. The vanishing theorems have a wide variety of applications and these are covered in detail. Of particular interest are the last three chapters, which are devoted to applications of the preceding material to the study of the structure and representations of complex semisimple Lie groups. Included are introductions to harmonic analysis, the Peter-Weyl theorem, Lie theory and the structure of Lie algebras, semisimple Lie algebras and their representations, algebraic groups and the structure of complex semisimple Lie groups. All of this culminates in Mili?i?'s proof of the Borel-Weil-Bott theorem, which makes extensive use of the material developed earlier in the text. There are numerous examples and exercises in each chapter. This modern treatment of a classic point of view would be an excellent text for a graduate course on several complex variables, as well as a useful reference for the expert.
Analytic Functions Of Several Complex Variables
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Author : Robert C. Gunning
language : en
Publisher: American Mathematical Society
Release Date : 2022-08-25
Analytic Functions Of Several Complex Variables written by Robert C. Gunning and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-25 with Mathematics categories.
The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. After initial successes by Poincaré and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for functions of one complex variable. Beginning in the 1930s, initially through the work of Oka, then H. Cartan, and continuing with the work of Grauert, Remmert, and others, new tools were introduced into the theory of several complex variables that resolved many of the open problems and fundamentally changed the landscape of the subject. These tools included a central role for sheaf theory and increased uses of topology and algebra. The book by Gunning and Rossi was the first of the modern era of the theory of several complex variables, which is distinguished by the use of these methods. The intention of Gunning and Rossi's book is to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces. Fundamental concepts and techniques are discussed as early as possible. The first chapter covers material suitable for a one-semester graduate course, presenting many of the central problems and techniques, often in special cases. The later chapters give more detailed expositions of sheaf theory for analytic functions and the theory of complex analytic spaces. Since its original publication, this book has become a classic resource for the modern approach to functions of several complex variables and the theory of analytic spaces. Further information about this book, including updates, can be found at the following URL: www.ams.org/publications/authors/books/postpub/chel-368.
Elementary Theory Of Analytic Functions Of One Or Several Complex Variables
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Author : Henri Cartan
language : en
Publisher: Courier Corporation
Release Date : 2013-04-22
Elementary Theory Of Analytic Functions Of One Or Several Complex Variables written by Henri Cartan and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Mathematics categories.
Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.
Several Complex Variables And Complex Geometry Part Ii
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Author : Eric Bedford
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
Several Complex Variables And Complex Geometry Part Ii written by Eric Bedford and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Several Complex Variables Maryland 1970 Proceedings Of The International Mathematical Conference Held At College Park April 6 17 1970
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Author : John Horvath
language : en
Publisher: Springer
Release Date : 2006-11-15
Several Complex Variables Maryland 1970 Proceedings Of The International Mathematical Conference Held At College Park April 6 17 1970 written by John Horvath and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.