Results 21 to 30 of about 3,261 (128)

Growth Estimates for Analytic Vector-Valued Functions in the Unit Ball Having Bounded $\mathbf{L}$-index in Joint Variables

Constructive Mathematical Analysis, 2020
Our results concern growth estimates for vector-valued functions of $\mathbb{L}$-index in joint variables which are analytic in the unit ball. There are deduced analogs of known growth estimates obtained early for functions analytic in the unit ball.Our estimates contain logarithm of $\sup$-norm instead of logarithm modulus of the function.They ...
Vita Baksa, Andriy Bandura, Oleh Skaskıv   +2 more
openaire   +5 more sources

Analytic in a polydisc functions of bounded $\mathbf{L}$-index in joint variables

Matematychni Studii, 2016
A. Bandura, N. Petrechko, O. Skaskiv
openaire   +2 more sources

Vector-Valued Entire Functions of Several Variables: Some Local Properties

Axioms, 2022
The present paper is devoted to the properties of entire vector-valued functions of bounded L-index in join variables, where L:Cn→R+n is a positive continuous function.
Andriy Ivanovych Bandura, Tetyana Mykhailivna Salo, Oleh Bohdanovych Skaskiv   +2 more
doaj   +1 more source

Maximum modulus in a bidisc of analytic functions of bounded $ L$-index and an analogue of Hayman's theorem [PDF]

Mathematica Bohemica, 2018
We generalize some criteria of boundedness of $\mathbf{L}$-index in joint variables for in a bidisc analytic functions. Our propositions give an estimate the maximum modulus on a skeleton in a bidisc and an estimate of $(p+1)$th partial derivative by ...
Andriy Bandura, Nataliia Petrechko, Oleh Skaskiv   +2 more
doaj   +1 more source

Entire multivariate vector-valued functions of bounded $\mathbf{L}$-index: analog of Fricke’s theorem

Математичні Студії, 2020
We consider a class of vector-valued entire functions $F\colon \mathbb{C}^{n}\rightarrow \mathbb{C}^{p}$. For this class of functions there is introduced a concept of boundedness of $\mathbf{L}$-index in joint variables. Let $|\cdot|_p$ be a norm in $
A. I. Bandura, V. P. Baksa
doaj   +1 more source

Exhaustion by balls and entire functions of bounded $\mathbf{L}$-index in joint variables

Ufimskii Matematicheskii Zhurnal, 2019
Summary: For entire functions of several complex variables, we prove criteria of boundedness of \(\mathbf{L} \)-index in joint variables. Here \(\mathbf{L}: \mathbb{C}^n\to\mathbb{R}^n_+\) is a continuous vector function. The criteria describe local behavior of partial derivatives of entire function on sphere in an \(n\)-dimensional complex space.
Bandura, Andriy Ivanovych, Skaskiv, Oleh Bohdanovych   +1 more
openaire   +2 more sources

Maximum modulus in a bidisc of analytic functions of bounded ${\bf L}$-index and an analogue of Hayman's theorem [PDF]

, 2018
summary:We generalize some criteria of boundedness of $\mathbf {L}$-index in joint variables for in a bidisc analytic functions. Our propositions give an estimate the maximum modulus on a skeleton in a bidisc and an estimate of $(p+1)$th partial ...
Petrechko, Nataliia, Skaskiv, Oleh, Bandura, Andriy   +2 more
core   +1 more source

Analytic functions in a bidisc of bounded $\mathbf{L}$-index in joint variables

, 2016
23 ...
Bandura, A. I., Petrechko, N. V., Skaskiv, O. B.   +2 more
openaire   +2 more sources

Composition of entire function and analytic functions in the unit ball with a vanished gradient

Математичні Студії
The composition $H(z)=f(\Phi(z))$ is studied, where $f$ is an entire function of a single complex variable and $\Phi$ is an analytic function in the $n$-dimensional unit ball with a vanished gradient. We found conditions by the function $\Phi$ providing
A. I. Bandura, T. M. Salo, O. B. Skaskiv
doaj   +1 more source

Uniform estimates for local properties of analytic functions in a complete Reinhardt domain

Математичні Студії
Using recent estimates of maximum modulus for partial derivatives of the analytic functions with bounded $\mathbf{L}$-index in joint variables we describe maximum modulus of these functions at the polydisc skeleton with given radii by the maximum modulus
A. I. Bandura, T.M. Salo
doaj   +1 more source