Illinois Journal of Mathematics

Reproducing kernel Hilbert spaces generated by the binomial coefficients

Daniel Alpay and Palle Jorgensen

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We study a reproducing kernel Hilbert space of functions defined on the positive integers and associated to the binomial coefficients. We introduce two transforms, which allow us to develop a related harmonic analysis in this Hilbert space. Finally, we mention connections with the theory of discrete analytic functions, statistics, and with the quantum case.

Article information

Illinois J. Math., Volume 58, Number 2 (2014), 471-495.

Received: 14 November 2013
Revised: 17 December 2014
First available in Project Euclid: 7 July 2015

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Zentralblatt MATH identifier

Primary: 46E22: Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32] 47H60: Multilinear and polynomial operators [See also 46G25] 11B65: Binomial coefficients; factorials; $q$-identities [See also 05A10, 05A30]


Alpay, Daniel; Jorgensen, Palle. Reproducing kernel Hilbert spaces generated by the binomial coefficients. Illinois J. Math. 58 (2014), no. 2, 471--495. doi:10.1215/ijm/1436275494.

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