Vol. 38, No. 2, 1971

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Schlicht mappings and infinitely divisible kernels

Roger Alan Horn

Vol. 38 (1971), No. 2, 423–430

The purpose of this note is to give a simple condition which is sufficient for a function on a real interval to be the boundary value of a schlicht (univalent) analytic mapping of the upper half plane into itself. This condition leads to a simple transformation which takes (possibly) non-schlicht mappings into schlicht ones. The methods used have applications to probability theory as well; they yield an interesting class of infinitely divisible characteristic functions.

Mathematical Subject Classification 2000
Primary: 30A24
Secondary: 60E05
Received: 20 August 1970
Published: 1 August 1971
Roger Alan Horn