Annales Academię Scientiarum Fennicę
Mathematica
Volumen 37, 2012, 649-660

FACTORIZATIONS OF ANALYTIC SELF-MAPS OF THE UPPER HALF-PLANE

Hari Bercovici and Dan Timotin

Indiana University, Department of Mathematics
Bloomington, IN 47405, U.S.A.; bercovic 'at' indiana.edu

Simion Stoilow Institute of Mathematics of the Romanian Academy
P.O. Box 1-764, Bucharest 014700, Romania; Dan.Timotin 'at' imar.ro

Abstract. We extend a factorization due to Krein to arbitrary analytic functions from the upper half-plane to itself. The factorization represents every such function as a product of fractional linear factors times a function which, generally, has fewer zeros and singularities than the original one. The result is used to construct functions with given zeros and poles on the real line.

2010 Mathematics Subject Classification: Primary 30H15.

Key words: Herglotz class, Krein factorization, interpolation.

Reference to this article: H. Bercovici and D. Timotin: Factorizations of analytic self-maps of the upper half-plane. Ann. Acad. Sci. Fenn. Math. 37 (2012), 649-660.

Full document as PDF file

doi:10.5186/aasfm.2012.3740

Copyright © 2012 by Academia Scientiarum Fennica