Umfang:
Online-Ressource
,
v.: digital
Ausgabe:
Online-Ausg. Springer eBook Collection. Mathematics and Statistics Electronic reproduction; Available via World Wide Web
ISBN:
9783034601252
Serie:
Operator Theory: Advances and Applications 192
Inhalt:
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.
Inhalt:
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.
Anmerkung:
Includes bibliographical references and index
,
CONTENTS; Preface; Introduction; Notation; 1 Elementary properties of holomorphic functions; 2 Solution of ?u = f and applications; 3 Splitting and factorization with respect to a contour; 4 The Rouché theorem for operator functions; 5 Multiplicative cocycles (O G -cocycles); 6 Families of subspaces; 7 Plemelj-Muschelishvili factorization; 8 Wiener-Hopf operators, Toeplitz operators and factorization; 9 Multiplicative cocycles with restrictions (F-cocycles); 10 Generalized interpolation problems; 11 Holomorphic equivalence, linearization and diagonalization; Bibliography; Index
,
Electronic reproduction; Available via World Wide Web
Weitere Ausg.:
ISBN 9783034601269
Weitere Ausg.:
ISBN 9783034601252
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Gohberg, Yiśrāʿēl Z., 1928 - 2009 Holomorphic operator functions of one variable and applications Basel : Birkhäuser, 2009 ISBN 9783034601252
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Operatorfunktion
;
Holomorphe Funktion
DOI:
10.1007/978-3-0346-0126-9
URL:
Volltext
(lizenzpflichtig)
Mehr zum Autor:
Gohberg, Yiśrāʿēl Z. 1928-2009
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