Accession Number:

AD0617864

Title:

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

Descriptive Note:

Corporate Author:

HARVARD UNIV CAMBRIDGE MASS

Personal Author(s):

Report Date:

1963-06-25

Pagination or Media Count:

38.0

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 Uas 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

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE