An Introduction to Analytic Multifunctions

Abstract

As we explained in the Preface this chapter will be a quick incursion, as the crow flies, into the important new field of analytic multifunctions. A complete treatment would need a full book. In particular it would be necessary to recall the great number of results we need in the theory of functions of several complex variables. Of course we are not able to do this, in such a limited number of pages, so we shall suppose that the reader is familiar with all these prerequisites, which are contained for instance in [5,9] or in many other books on the field, and which are summarized in the Appendix, §2. In the last ten years the use of subharmonic functions in spectral theory and in the theory of uniform algebras has given a lot of interesting new results (see Chapters III and V for spectral theory; Exercises VII.8–9–10 and [10] for the theory of uniform algebras).