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PÓLYA CLASS THEORY FOR HERMITE–BIEHLER FUNCTIONS OF FINITE ORDER

Published online by Cambridge University Press:  25 September 2003

MICHAEL KALTENBÄCK  and
HARALD WORACEK
MICHAEL KALTENBÄCK
Affiliation:
Institute for Analysis and Technical Mathematics, Technical University of Vienna, Wiedner Hauptstraße 8–10, 1040 Wien, [email protected]
HARALD WORACEK
Affiliation:
Institute for Analysis and Technical Mathematics, Technical University of Vienna, Wiedner Hauptstraße 8–10, 1040 Wien, [email protected]
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Abstract

A partition of the class of all Hermite–Biehler entire functions of finite order into subclasses ${\cal P}_\kappa$ is introduced. A given function $E(z)$ belongs to ${\cal P}_\kappa$ if and only if $-z^{-1}\log E(z)\in{\mc N}_\kappa$, where the class ${\mc N}_\kappa$ is a well studied family of meromorphic functions on the upper half plane, which originates from operator theoretic problems. It is also proved that the subclasses ${\cal P}_\kappa$ are stable under bounded type perturbation.

Keywords

30D1530D1046C20
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 68 , Issue 2 , October 2003 , pp. 338 - 354
Copyright
The London Mathematical Society 2003

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