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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hermite-Biehler functions with zeros close to the imaginary axis


Authors: Michael Kaltenbäck and Harald Woracek
Journal: Proc. Amer. Math. Soc. 133 (2005), 245-255
MSC (2000): Primary 46E20, 46E22; Secondary 30H05, 30D15
Published electronically: August 4, 2004
MathSciNet review: 2086217
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Abstract: A Hermite-Biehler function $E$ gives rise to a de Branges Hilbert space $\mathcal{H}(E)$ consisting of entire functions. We are going to show that for Hermite-Biehler functions of sufficiently small growth and a certain distribution of zeros every proper de Branges subspace of $\mathcal{H}(E)$ coincides for some $n\in\mathbb{N}$ with the $(n+1)$-dimensional linear space of all polynomials of degree at most $n$.


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Additional Information

Michael Kaltenbäck
Affiliation: Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstr. 8–10/101, A–1040 Wien, Austria
Email: michael.kaltenbaeck@tuwien.ac.at

Harald Woracek
Affiliation: Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstr. 8–10/101, A–1040 Wien, Austria
Email: harald.woracek@tuwien.ac.at

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07605-1
PII: S 0002-9939(04)07605-1
Received by editor(s): March 15, 2003
Received by editor(s) in revised form: October 7, 2003
Published electronically: August 4, 2004
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 American Mathematical Society