Daniel Alpay

Mihaela B. Vajiac

David Shoikhet

Ronen Peretz

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.

Chapman University, November 2019

New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative

Mark Agranovsky

Anatoly Golberg

Fiana Jacobzon

Lawrence Zalcman

This book focuses on developments in complex dynamical systems and geometric function theory over the past decade, showing strong links with other areas of mathematics and the natural sciences. Traditional methods and approaches surface in physics and in the life and engineering sciences with increasing frequency – the Schramm‐Loewner evolution, Laplacian growth, and quadratic differentials are just a few typical examples. This book provides a representative overview of these processes and collects open problems in the various areas, while at the same time showing where and how each particular topic evolves. This volume is dedicated to the memory of Alexander Vasiliev.

New Trends and Open Problems

Complex Analysis and Dynamical Systems

David Shoikhet

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