THE MULTIPLICATIVE STRUCTURE AND CHARACTERISTIC SETS OF HOLOMORPHIC NOETHERIAN OPERATOR-VALUED FUNCTIONS

Abstract

It is shown that a holomorphic Noetherian operator-valued function defined in a neighborhood of a holomorphically convex compact set in a Stein space can be written as a product of factors, one for each irreducible branch of the characteristic set. A dual result is also proved. The principal results were announced in Dokl. Akad. Nauk SSSR 203 (1972), 1255–1257=Soviet Math. Dokl. 13 (1972), 546–549. Bibliography: 13 items.