On Existence of Main Polynomial for Analytic Vector-Valued Functions of Bounded L-Index in the Unit Ball

Abstract

In this paper, we present necessary and sufficient conditions of boundedness of L-index in joint variables for vector-functions analytic in the unit ball, where L = (l 1 , l 2 ) :These conditions describe local behavior of homogeneous polynomials (so-called a main polynomial) with power series expansion for analytic vector-valued functions in the unit ball. These results use a bidisc exhaustion of a unit ball.Key words and phrases: bounded index, bounded L-index in joint variables, analytic function, unit ball, main polynomial, homogeneous polynomial.