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# Operator Theory: Advances and Applications #192: Holomorphic Operator Functions of One Variable and Applications: Methods from Complex Analysis in Several Variables

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 Comment on this title and you could win free books!Synopses & Reviews Table of Contents ISBN13: 9783034601252 ISBN10: 3034601255 Condition: All Product Details

### Synopses & Reviews

This is a book on holomorphic operator functions of a single variable and applications, which is focused on the relations between local and global theories. It is based on methods and technics of complex analysis of several variables. The first part of the theory starts with a straightforward generalization of some results from the basics of analysis of scalar functions of one complex variable. In the second part, which is the main part of the theory, results are obtained by methods and tools adapted from complex analysis of functions of several variables. We have in mind the theory of holomorphic cocycles (fiber bundles) with values in infinite-dimensional non-commutative groups. As a rule, these results do not appear in traditional complex analysis of one variable, not even for matrix valued cocycles. The third part consists of applications to operator theory. Here applications are presented for holomorphic families of subspaces and Plemelj-Muschelishvili factorization. The fourth part presents a generalization of the theory of cocycles to cocycles with restrictions. This part contains also applications to interpolation problems, to the problem of holomorphic equivalence and diagonalization.

#### Synopsis:

This book presents holomorphic operator functions of a single variable and applications, which are focused on the relations between local and global theories. It is based on methods and technics of complex analysis of several variables.

Preface.- Introduction.- 1. Elementary Properties of Holomorphic Functions.- 2. Solution of \bar\partial u=f and Applications.- 3. Splitting and Factorization w.r.t. a Contour.- 4. The Rouché Theorem for Operator Functions.- 5. Multiplicative Cocycles.- 6. Families of Subspaces.- 7. Plemelj-Muschelishvili Factorization.- 8. Wiener-Hopf Operators, Toeplitz Operators and Factorizations.- 9. Multiplicative Cocycles with Restrictions.- 10. Generalized Interpolation Problems.- 11. Holomorphic Equivalence, Linearization and Diagonalization.- Bibliography.- Index

### Product Details

ISBN:
9783034601252
Author:
Publisher:
Birkhauser Basel
Author:
Author:
Author:
Author:
Author:
Author:
Author:
Author:
Location:
Basel
Subject:
Functional Analysis
Subject:
Mathematical Analysis
Subject:
Cocycles
Subject:
Factorization
Subject:
holomorphic function
Subject:
operator function
Subject:
Functions of a complex variable.
Subject:
Operator theory
Subject:
Mathematics : Functional Analysis
Subject:
Mathematics
Subject:
The Arts
Subject:
mathematics and statistics
Subject:
Functions of complex variables
Edition Description:
Book
Series:
Series Volume:
192
Publication Date:
20090806
Binding:
HARDCOVER
Language:
English
Pages:
444
Dimensions:
235 x 165 mm