
Accession Number : AD0617864
Title : LINEAR INVARIANT FAMILIES OF ANALYTIC FUNCTIONS, PART II (LINEARINVARIANTE 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 pvalent 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