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...

This volume collects two articles by Christine Laurent-Thiebaut and Jurgen Leiterer which were submitted to, and accepted by the Annali della Scuola Normale Superiore, Classe di Scienze: The q-convex case; the q-concave case. Owing to the character of the systematic exposition of the new scientific results achieved and to the size of the work, the authors agreed to have the two papers published in a separate volume.