Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 58, Number 2 (2014), 471-495.
Reproducing kernel Hilbert spaces generated by the binomial coefficients
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.
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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Mathematical Reviews number (MathSciNet)
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. https://projecteuclid.org/euclid.ijm/1436275494