Accession Number:

AD0257057

Title:

ON THE GEOMETRY OF FUNCTIONS HOLOMORPHIC IN THE UNIT CIRCLE, OF ARBITRARILY SLOW GROWTH, WHICH TEND TO INFINITY ON A SEQUENCE OF CURVES APPROACHING THE CIRCUMFERENCE

Descriptive Note:

Corporate Author:

RICE UNIV HOUSTON TEX

Personal Author(s):

Report Date:

1961-04-01

Pagination or Media Count:

1.0

Abstract:

IT IS WELL KNOWN THAT THERE EXIST FUNCTIONS H , holomorphic in 1, with H where r is a given positive function which as r 1, and such that min rn H approaches as n . Here rn 1 is an appropriately chosen sequence. Such functions may be constructed by the use of gap series or via an infinite product. The object of the present note is to construct such a function geometrically by starting with the Riemann surface onto which w H maps 1. The essence of the argument is in showing that is hyperbolic and that Mr r these results are obtained via Caratheodorys theory of kernels. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE