Title

Reproducing Kernel Hilbert Spaces Generated by the Binomial Coefficients

Document Type

Article

Publication Date

2014

Abstract

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.

Comments

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Illinois Journal of Mathematics, volume 58, in 2014 following peer review. The definitive publisher-authenticated version is available online at Project Euclid.

Peer Reviewed

1

Copyright

Board of Trustees of the University of Illinois