New Directions in Function Theory: From Complex to Hypercomplex to Non Commutative : Chapman University November 2019 Editorial Introduction On Parseval Frames of Kernel Functions in de Branges Spaces of Entire Vector Valued Functions Differential Subordinations in Harmonic Mappings The Segal Bargmann Transform in Clifford Analysis On the Carathéodory Fejér interpolation problem for Stieltjes functions Harmonic Analysis of some arithmetical functions Symmetric measures continuous networks and dynamics Multi Variable Semicircular Processes From Homomorphisms and Operators Representation formulae for the determinant in a neighborhood of the identity Parametrization of the Solution Set of a Matricial Truncated Hamburger Moment Problem by a Schur Type Algorithm The Wiener algebra and singular integrals Techniques to derive estimates for integral means and other geometric quantities related to conformal mappings Complex Ternary Analysis and Applications. This volume presents selected contributions from experts gathered at Chapman University for a conference held in November 2019 on new directions in function theory. The papers written by leading researchers in the field relate to hypercomplex analysis Schur analysis and de Branges spaces new aspects of classical function theory and infinite dimensional analysis. Signal processing constitutes a strong presence in several of the papers. A second volume in this series of conferences this book will appeal to mathematicians interested in learning about new fields of development in function theory.