Smale's mean value conjecture for finite Blaschke products

Abstract

Motivated by a dictionary between polynomials and finite Blaschke products, we study both Smale's mean value conjecture and its dual conjecture for finite Blaschke products in this paper. Our result on the dual conjecture for finite Blaschke products allows us to improve a bound obtained by V. Dubinin and T. Sugawa for the dual mean value conjecture for polynomials.

To appear in an issue of Journal of Analysis denoted to the Proceedings of the Conference on Modern Aspects of Complex Geometry (MindaFest))