Abstract
We study solutions to convolution equations for functions with discrete support in ℝn, a special case being functions with support in the integer points. The Fourier transform of a solution can be extended to a holomorphic function in some domains in ℂn, and we determine possible domains in terms of the properties of the convolution operator.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Banderier C, Schwer S. Why Delannoy numbers? J Statist Plann Inference, 2005, 135: 40–54
Bourbaki N. Topologie générale, chapters 1. and 2. Éléments de mathématique, Première partie, 3rd ed. Paris: Hermann, 1961
Delannoy H. Emploi de l’échiquier pour la résolution de certains problèmes de probabilité. C R Congr Annu Assoc Franc Sci, 1895, 24: 70–90
Ehrenpreis L. Solution of some problems of division, I: Division by a polynomial of derivation. Amer J Math, 1954, 76: 883–903
Kiselman C O. Functions on discrete sets holomorphic in the sense of Ferrand, or monodiffric functions of the second kind. Sci China Ser A, 2008, 51: 604–619
Kiselman C O. Estimates for solutions to discrete convolution equations. Mathematika, 2015, 61: 295–308
Pemantle R, Wilson M C. Asymptotics of multivariate sequences, I: Smooth points of the singular variety. J Combin Theory Ser A, 2002, 97: 129–161
Samieinia S. The number of continuous curves in digital geometry. Port Math, 2010, 67: 75–89
Schwer S R, Autebert J-M. Henri-Auguste Delannoy, une biographie. Math Sci Hum Math Soc Sci, 2006, 174: 25–67
Sulanke R A. Objects counted by the central Delannoy numbers. J Integer Seq, 2003, 6: Article 03.1.5, 19pp
Vassilev M, Atanassov K. On Delanoy numbers. Annuaire Univ Sofia Fac Math Inform, 1987, 81: 153–162
Author information
Authors and Affiliations
Corresponding author
Additional information
In memory of Professor LU QiKeng (1927–2015)
Rights and permissions
About this article
Cite this article
Kiselman, C.O. Domains of holomorphy for Fourier transforms of solutions to discrete convolution equations. Sci. China Math. 60, 1005–1018 (2017). https://doi.org/10.1007/s11425-015-9029-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11425-015-9029-0