Annales AcademiŠ Scientiarum FennicŠ
Mathematica
Volumen 35, 2010, 23-46

COMPLETE INTERPOLATING SEQUENCES, THE DISCRETE MUCKENHOUPT CONDITION, AND CONFORMAL MAPPING

Gunter Semmler

TU Bergakademie Freiberg, Institut fŘr Angewandte Analysis
PrŘferstrasse 9, 09596 Freiberg, Germany; semmler 'at' math.tu-freiberg.de

Abstract. We extend the parameterization of sine-type functions in terms of conformal mappings onto slit domains given by Eremenko and Sodin to the more general case of generating functions of real complete interpolating sequences. It turns out that the cuts have to fulfill the discrete Muckenhoupt condition studied earlier by Lyubarskii and Seip.

2000 Mathematics Subject Classification: Primary 42A65, 30D15, 30C20.

Key words: Complete interpolating sequences, nonharmonic Fourier series, Riesz basis of exponentials, generating function, interpolation in Paley-Wiener spaces, discrete Muckenhoupt condition, sine-type function.

Reference to this article: G. Semmler: Complete interpolating sequences, the discrete Muckenhoupt condition, and conformal mapping. Ann. Acad. Sci. Fenn. Math. 35 (2010), 23-46.

Full document as PDF file

doi:10.5186/aasfm.2010.3502

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