Rocky Mountain Journal of Mathematics
- Rocky Mountain J. Math.
- Volume 49, Number 4 (2019), 1063-1092.
Functions analytic in the unit ball having bounded $L$-index in a direction
We propose a generalization of a concept of bounded index for analytic functions in the unit ball. Use of directional derivatives gives us a possibility to deduce the necessary and sufficient conditions of boundedness of $L$-index in a direction for analytic functions of several variables, namely, we obtain an analog of Hayman's theorem and a logarithmic criteria for this class. The criteria describe the behavior of the directional logarithmic derivative outside the zero set and a uniform distribution of zeros in some sense. The criteria are useful for studying analytic solutions of partial differential equations and estimating their growth. We present a scheme of this application.
Rocky Mountain J. Math., Volume 49, Number 4 (2019), 1063-1092.
First available in Project Euclid: 29 August 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Bandura, Andriy; Skaskiv, Oleh. Functions analytic in the unit ball having bounded $L$-index in a direction. Rocky Mountain J. Math. 49 (2019), no. 4, 1063--1092. doi:10.1216/RMJ-2019-49-4-1063. https://projecteuclid.org/euclid.rmjm/1567044028