On Discrete Analytic Functions: Products, Rational Functions, and Reproducing Kernels

Authors

Daniel Alpay, Chapman UniversityFollow
Palle Jorgensen, University of Iowa
Ron Seager, Kansas State University
Dan Volok, Kansas State University

Document Type

Article

Publication Date

2013

Abstract

We introduce a family of discrete analytic functions, called expandable discrete analytic functions, which includes discrete analytic polynomials, and define two products in this family. The first one is defined in a way similar to the Cauchy-Kovalevskaya product of hyperholomorphic functions, and allows us to define rational discrete analytic functions. To define the second product we need a new space of entire functions which is contractively included in the Fock space. We study in this space some counterparts of Schur analysis.

Comments

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Journal of Applied Mathematics and Computing, volume 41, issue 1, in 2013 following peer review. The final publication is available at Springer via DOI: 10.1007/s12190-012-0608-2

Recommended Citation

,D. Alpay, P. Jorgensen, R. Seager, and D. Volok. On discrete analytic functions: Products, Rational Functions, and Reproducing Kernels. Journal of Applied Mathematics and Computing. Volume 41, Issue 1 (2013), Page 393-426.

Peer Reviewed

1

Copyright

Springer