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On discrete analytic functions: Products, rational functions and reproducing kernels |
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| Authors: | Daniel Alpay Palle Jorgensen Ron Seager Dan Volok |
| Affiliation: | 1. Department of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, Be’er Sheva, 84105, Israel 2. Department of Mathematics, The University of Iowa, 14 MLH, Iowa City, IA, 52242-1419, USA 3. Mathematics Department, Kansas State University, 138 Cardwell Hall, Manhattan, KS, 66506, USA |
| 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. |
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