Accession Number : AD0617864

Title :   LINEAR INVARIANT FAMILIES OF ANALYTIC FUNCTIONS, PART II (LINEAR-INVARIANTE FAMILIEN ANALYTISCHER FUNKTIONEN II),

Corporate Author : HARVARD UNIV CAMBRIDGE MASS

Personal Author(s) : Pommerenke,Christian

Report Date : 25 JUN 1963

Pagination or Media Count : 38

Abstract : This paper considers normal families M of functions that are analytic, locally univalent, and normalized in the unit disk. These families are assumed to satisfy a certain invariance property. The prime example is the family U of normalized univalent functions. Another example is the family of locally univalent p-valent functions. In the first part, general properties of these families are studied. For instance, the distortion theorems for U can be generalized to the families M. If the family M is of uniformly bounded characteristic (as ins U)(as is U) then a number of geometric properties can be established, several of which are new even for the case U. In the second part, the boundary behavior of functions in M is investigated, using a certain sequence of functions again in M. Several types of boundary behavior are described and studied. (Author)

Descriptors :   (*FUNCTIONS(MATHEMATICS), INVARIANCE), GEOMETRY, THEORY

Distribution Statement : APPROVED FOR PUBLIC RELEASE