Holomorphic operator functions of one variable and applications: methods from complex analysis in several variables

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 ofsome 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 areobtained 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 tooperator theory. Here applications are presented for holomorphic families of subspaces and Plemelj-Muschelishvili factorization. The forth part presents a generalization of the theory of cocycles to cocycles with restrictions. Applications deal with interpolation, holomorphic families of subspaces and frames, holomorphic equivalence and diagonalization and Plemlj-Muschelishvili factorization Exposition of the material is made in style and terms which are used in Complex analysis of several variables INDICE: Preface.- Introduction.- 1. Elementary Properties of Holomorphic Functions.- 2. Solution of arpartial u=f and Applications.- 3. Splitting andFactorization 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

• ISBN: 978-3-0346-0125-2
• Editorial: Birkhaüser
• Encuadernacion: Cartoné
• Páginas: 445
• Fecha Publicación: 01/07/2009
• Nº Volúmenes: 1
• Idioma: Inglés