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Other titles in the Operator Theory: Advances and Applications series:

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

by

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

 

Synopses & Reviews

Publisher Comments:

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.

Table of Contents

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:
Gohberg, Israel
Publisher:
Birkhauser Basel
Author:
Leiterer, Jurgen
Author:
&
Author:
rgen Leiterer
Author:
uuml
Author:
Leiterer, J
Author:
rgen
Author:
Leiterer, Ja1/4rgen
Author:
J
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
Copyright:
Edition Description:
Book
Series:
Operator Theory: Advances and Applications
Series Volume:
192
Publication Date:
20090806
Binding:
HARDCOVER
Language:
English
Pages:
444
Dimensions:
235 x 165 mm

Related Subjects

Engineering » Civil Engineering » General
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Operator Analysis

Operator Theory: Advances and Applications #192: Holomorphic Operator Functions of One Variable and Applications: Methods from Complex Analysis in Several Variables New Hardcover
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Product details 444 pages Birkhauser Basel - English 9783034601252 Reviews:
"Synopsis" by , 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.
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