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.
Recommended Citation
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.
Peer Reviewed
1
Copyright
Board of Trustees of the University of Illinois
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.