Mini-Workshop: Complex Approximation and Universality

Abstract

The mini-workshop was devoted to the study of universality in connection with approximation theory in complex analysis and related notions within the framework of Banach spaces and various function spaces. Topics discussed included invariance of universality, Baire category and universality, the size and structure of the set of universal functions, universality for composition with respect to a sequence of mappings, universal Taylor series and Faber series, overconvergent series, lacunary series, holomorphic continuation of series, universal series with restricted coefficients, universality for solutions of the Laplace equation, the heat equation and Burgers’ equation, hypercyclicity, and superhypercyclicity. Topics in approximation included polynomial approximation, approximation and maximum principles, approximating inner functions by Blaschke products, and approximation of the Riemann zeta function. A list of open problems is included in the report.