Hermite-Biehler functions with zeros close to the imaginary axis
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- by Michael Kaltenbäck and Harald Woracek PDF
- Proc. Amer. Math. Soc. 133 (2005), 245-255 Request permission
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 $n$.References
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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
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 245-255
- MSC (2000): Primary 46E20, 46E22; Secondary 30H05, 30D15
- DOI: https://doi.org/10.1090/S0002-9939-04-07605-1
- MathSciNet review: 2086217