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.
D. Alpay and P. Jorgensen. Reproducing kernel Hilbert spaces generated by the binomial coefficients. Illinois Journal of Mathematics, vol. 58 (2014), no. 2, 471-495.
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