Discrete analytic functions and Schur analysis

Abstract: We introduce the Schur class of functions, discrete analytic on the integer lattice in the complex plane. As a special case, we derive the explicit form of discrete analytic Blaschke factors and solve the related basic interpolation problem. We define and study rational discrete analytic functions and prove the existence of a coisometric realization for discrete analytic Schur multipliers. The talk is based on collaborations with F. Colombo, K. Diki, I. Sabadini and D. Volok.

analysis of PDEsclassical analysis and ODEscomplex variablesdifferential geometrydynamical systemsfunctional analysismetric geometry

Audience: researchers in the topic

Analysis and Geometry Seminar