α-normal functions and yosida functions

Abstract

α-normal functions, α ≥ 1, are meromorphic functions in the unit disk D with α-normal functions (α>1) are characterized by the normality of a family of functions on compact subsets of the finite complex plane . We prove that limit functions of converging sequences of functions {fn (ζ)} are Yosida's functions. We extract a subclass of the α-normal functions such that limit functions of converging sequences of functions are Yosida's functions of the first kind. Note that meromorphic solutions of algebraic differential equations of the first order with coefficients from the Hardy spaces Hp are a-normal functions.