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Catalogue Information
Field name	Details
Dewey Class	515.9
Title	Holomorphic Operator Functions of One Variable and Applications ([Ebook]) : Methods from Complex Analysis in Several Variables / by Israel Gohberg, Jürgen Leiterer.
Author	Gohberg, Israel , 1928-2009
Added Personal Name	Leiterer, Jürgen
Other name(s)	SpringerLink (Online service)
Publication	Basel : Birkhäuser , 2009.
Physical Details	: 1 online resource.
Series	Operator theory : advances and applications ; 192
ISBN	9783034601269
Summary Note	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.:
Contents note	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 RouchÃ© 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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-0346-0126-9
Links to Related Works	Subject References: Functions of a Complex Variable . Functions of complex variables . Mathematics . Operator Theory . Authors: author . Gohberg, Israel 1928-2009 . Leiterer, Jürgen . Corporate Authors: SpringerLink (Online service) . Series: Operator theory : advances and applications . Classification: 515.9 . 515.9 (DDC 23) .

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

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