Taylor Series of the Natural Powers of the Pick Function and Applications
The analytic theory of matrix orthogonal polynomials.
The length of a lemmiscate.
The logarithmic asymptotic expansions for the norms of evaluation functionals.
The roots of a polynomial depend continuously on its coefficients.
The Schwarz-Pick theorem and its applications
Various derivative estimates for functions of exponential type in a half-plane are proved in this paper. The reader will also find a related result about functions analytic in a quadrant. In addition, the paper contains a result about functions analytic in a strip. Our main tool in this study is the Schwarz-Pick theorem from the geometric theory of functions. We also use the Phragmén-Lindelöf principle, which is of course standard in such situations.