Identifiant pérenne de la notice : 215212827
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Note publique d'information : 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
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