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arXiv · 1208.3699

On discrete analytic functions: Products, Rational Functions, and some Associated Reproducing Kernel Hilbert Spaces

Daniel Alpay·Palle Jorgensen·Ron Seager·Dan Volok
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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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Daniel Alpay, Palle Jorgensen, Ron Seager, Dan Volok. 2012-08-17. On discrete analytic functions: Products, Rational Functions, and some Associated Reproducing Kernel Hilbert Spaces. https://arxiv.org/abs/1208.3699

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