This contains 15 (survey and research) papers presented at the conference Blaschke products and their applications held at the Fields Institute in Toronto July 25-29, 2011.
This is a selection of papers presented at the the conference Blaschke products and their applications held at the Fields Institute in Toronto July 25-29, 2011. It is volume 65 of the Series Fields Institute Communications.
Blaschke products were introduced by Blaschke in 1915 to study analytic functions in the complex unit disk. These (infinite) products are examples of inner functions, i.e., functions analytic in the unit disk with boundary value 1 a.e. A similar definition exists for functions analytic in the upper half plane. Blaschke products may collect the zeros of of functions in Hardy spaces and are therefore an essential element of inner-outer factorization of these functions.
Blaschke functions and their derivatives appeared in several applications like approximation theory, solution of extremal problems, operator theory, differential equations, geometry, and even computability theory. Some of these applications are treated in the contributions of these proceedings. Among the fifteen papers are a few survey papers which are usually longer, but most of them are shorter research-type papers. The titles with a one-sentence description are as follows. Even if the title does not mention it explicitly, all these papers involve Blaschke products one way or another.
The book is of interest both to students and researchers who need the theory of complex functions and especially those who are working in Hardy and related spaces.