ENGLISH

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

By Israel Gohberg , Jürgen Leiterer

Book information

Publisher
Birkhäuser Basel
Year
2009
ISBN
3034601255, 9783034601252
Language
english
Format
PDF
Filesize
3 MB (3169087 bytes)
Series
Operator Theory: Advances and Applications
Edition
1
Pages
435\435
Time added
2010-10-13 10:14:08

Description

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.

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