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

2012/08/17 by Daniel Alpay, Palle Jorgensen, Palle E. T. Jørgensen +6
Mathematics · #20G43 #30H20 #32A26 #43A22 #46E22 #46L08 #47B32 #47B39 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Primary 30G25 #advanced mathematical theories #math.CV #math.FA #msc:20G43 #msc:30G25 #msc:30H20 #msc:32A26 #msc:43A22 #msc:46E22 #msc:46L08 #msc:47B32 #msc:47B39

paper · pdf · doi:10.48550/arxiv.1208.3699

arxiv created 2012/08/17 · openalex publication_date 2012/08/17 · arxiv updated 2012/08/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Related

• Schur analysis and discrete analytic functions: Rational functions and co-isometric realizations
• Discrete analytic Schur functions
• Discrete analytic functions, structured matrices and a new family of moment problems
• Infinite product representations for kernels and iterations of functions
• Reproducing kernel Hilbert spaces generated by the binomial coefficients