Interpolation of entire functions on regular sparse sets and q -Taylor series

Michael Welter[1]

  • [1] Mathematisches Institut der Universität Bonn Beringstr. 4 53115 Bonn, Allemagne

Journal de Théorie des Nombres de Bordeaux (2005)

  • Volume: 17, Issue: 1, page 397-404
  • ISSN: 1246-7405

Abstract

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We give a pure complex variable proof of a theorem by Ismail and Stanton and apply this result in the field of integer-valued entire functions. Our proof rests on a very general interpolation result for entire functions.

How to cite

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Welter, Michael. "Interpolation of entire functions on regular sparse sets and $q$-Taylor series." Journal de Théorie des Nombres de Bordeaux 17.1 (2005): 397-404. <http://eudml.org/doc/249438>.

@article{Welter2005,
abstract = {We give a pure complex variable proof of a theorem by Ismail and Stanton and apply this result in the field of integer-valued entire functions. Our proof rests on a very general interpolation result for entire functions.},
affiliation = {Mathematisches Institut der Universität Bonn Beringstr. 4 53115 Bonn, Allemagne},
author = {Welter, Michael},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
number = {1},
pages = {397-404},
publisher = {Université Bordeaux 1},
title = {Interpolation of entire functions on regular sparse sets and $q$-Taylor series},
url = {http://eudml.org/doc/249438},
volume = {17},
year = {2005},
}

TY - JOUR
AU - Welter, Michael
TI - Interpolation of entire functions on regular sparse sets and $q$-Taylor series
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 1
SP - 397
EP - 404
AB - We give a pure complex variable proof of a theorem by Ismail and Stanton and apply this result in the field of integer-valued entire functions. Our proof rests on a very general interpolation result for entire functions.
LA - eng
UR - http://eudml.org/doc/249438
ER -

References

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  1. J.-P. Bézivin, Sur les points où une fonction analytique prend des valeurs entières. Ann. Inst. Fourier 40 (1990), 785–809. Zbl0719.30022MR1096591
  2. J.-P. Bézivin, Fonctions entières prenant des valeurs entières ainsi que ses dérivées sur des suites recurrentes binaires. Manuscripta math. 70 (1991), 325–338. Zbl0733.30022MR1089068
  3. P. Bundschuh, Arithmetische Eigenschaften ganzer Funktionen mehrerer Variablen. J. reine angew. Math. 313 (1980), 116–132. Zbl0411.10009MR552466
  4. M. E. H. Ismail, D. Stanton, q -Taylor theorems, polynomial expansions, and interpolation of entire functions. Journal of Approximation Theory 123 (2003), 125–146. Zbl1035.30025MR1985020
  5. S. Lang, Algebra. 3rd edition, Addison-Wesley (1993). Zbl0848.13001MR197234
  6. M. Welter, Ensembles régulièrement lacunaires d’entiers et fonctions entières arithmétiques. J. Number Th. 109 (2004), 163–181. Zbl1068.30020MR2098482

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