Holomorphic Operator Functions of One Variable and Applications

Gohberg, Prof. Israel; Leiterer, Jurgen

ISBN 10: 3034601255 / ISBN 13: 9783034601252

Editore: Birkhauser Verlag AG, 2009

Riguardo questo articolo

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. Series: Operator Theory: Advances and Applications. Num Pages: 444 pages, biography. BIC Classification: PBKF. Category: (P) Professional & Vocational. Dimension: 244 x 170 x 28. Weight in Grams: 945. . 2009. Hardback. . . . . Books ship from the US and Ireland.

Codice articolo V9783034601252

Dati bibliografici

• Titolo: Holomorphic Operator Functions of One Variable and Applications
• Editore: Birkhauser Verlag AG
• Data di pubblicazione: 2009
• Lingua: Inglese
• ISBN 10: 3034601255
• ISBN 13: 9783034601252
• Rilegatura: Rilegato
• Condizione: New

Descrizione articolo

Riassunto

This is a book on holomorphic operator functions of a single variable and their - plications,whichisfocussedontherelationsbetweenlocalandglobaltheories.Itis based on methods and technics of Complex analysis of scalar and matrix functions of several variables. The applications concern: interpolation, holomorphic families of subspaces and frames, spectral theory of polynomials with operator coe?cients, holomorphic equivalence and diagonalization, and Plemelj-Muschelishvili fact- ization. The book also contains a theory of Wiener-Hopf integral equations with operator-valued kernels and a theory of in?nite Toplitz ¨ matrices with operator entries. We started to work on these topics long ago when one of us was a Ph.D. s- dent of the other in Kishinev (now Cisinau) University. Then our main interests were in problems of factorization of operator-valued functions and singular in- gral operators. Working in this area, we realized from the beginning that di?erent methods and tools from Complex analysis of several variables and their modi?- tions are very useful in obtaining results on factorization for matrix and operator functions. We have in mind di?erent methods and results concerning connections between local and global properties of holomorphic functions. The ?rst period was very fruitful and during it we obtained the basic results presented in this book.

Contenuti

Elementary properties of holomorphic functions.- Solution of and applications.- Splitting and factorization with respect to a contour.- The Rouché theorem for operator functions.- Multiplicative cocycles ( -cocycles).- Families of subspaces.- Plemelj-Muschelishvili factorization.- Wiener-Hopf operators, Toeplitz operators and factorization.- Multiplicative cocycles with restrictions ( -cocycles).- Generalized interpolation problems.- Holomorphic equivalence, linearization and diagonalization.