Holomorphic Operator Functions of One Variable and Applications Israel Gohberg

ISBN: 9783034601276

Published: August 28th 2009

Paperback

446 pages


Description

Holomorphic Operator Functions of One Variable and Applications  by  Israel Gohberg

Holomorphic Operator Functions of One Variable and Applications by Israel Gohberg
August 28th 2009 | Paperback | PDF, EPUB, FB2, DjVu, AUDIO, mp3, RTF | 446 pages | ISBN: 9783034601276 | 8.26 Mb

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 partMoreThis 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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