11 citations · 26 across the 16 of their papers we have counts for
6 papers · 1 filter
Schur analysis and discrete analytic functions: Rational functions and co-isometric realizations
Daniel Alpay, Dan Volok
We define and study rational discrete analytic functions and prove the existence of a coisometric realization for discrete analytic Schur multipliers.
A new realization of rational functions, with applications to linear combination interpolation
Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz +1
We introduce the following linear combination interpolation problem (LCI): Given distinct numbers and complex numbers and , find all…
On discrete analytic functions: Products, Rational Functions, and some Associated Reproducing Kernel Hilbert Spaces
Daniel Alpay, Palle Jorgensen, Ron Seager +1
We introduce a family of discrete analytic functions, called expandable discrete analytic functions, which includes discrete analytic polynomials, and define two products in this f…
Caratheodory-Fejer interpolation and related topics in locally convex spaces
Daniel Alpay, Olga Timoshenko, Dan Volok
We study Caratheodory-Herglotz functions whose values are continuous operators from a locally convex topological space which admits the factorization property into its conjugate du…
Carathéodory functions in the Banach space setting
Daniel Alpay, Olga Timoshenko, Dan Volok
We prove representation theorems for Carathéodory functions in the setting of Banach spaces.
Rational hyperholomorphic functions in (\mathbb R^4)
D. Alpay, M. Shapiro, D. Volok
We introduce the notion of rationality for hyperholomorphic functions (functions in the kernel of the Cauchy-Fueter operator). Following the case of one complex variable, we give t…