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 and with the quantum case. 
Daniel Alpay and Palle Jorgensen
math.CV math.FA