On Approximation and Generalized Type of Analytic Functions of Several Complex Variables

Abstract

In the present paper, we study the polynomial approximation of analytic functions of several complex variables. The characterizations of generalized type of analytic functions of several complex variables have been obtained in terms of approximation and interpolation errors.

Basics on growth orders of polymonogenic functions

“…In parallel other generalizations of the notions of growth orders and types have been introduced in the very recent works of Srivastava and Kumar, cf. [16][17][18]. This has been done first in the context of a class of elliptic equations in one complex variable, after that in the setting of several complex variables and finally for entire monogenic functions which reflects the increasing recent interest in this research topic.…”

Criterion of the continuation of harmonic functions in the ball of n­dimensional space and representation of the generalized orders of the entire harmonic functions in ℝn in terms of approximation error

“…UDC 517.572 DOI: 10.15587/1729-4061.2017.108387 orders for the entire functions of two complex variables were introduced and investigated in [5]. Similar problems were considered for analytic functions of several complex variables in [6,7].…”

The Growth of Generalized Hadamard Product of Entire Axially Monogenic Functions

“…The rst direction is the study of the asymptotic growth behavior of the entire functions of several complex variables (see e.g. [12,13,17,20]). The second one is devoted to the integral functions of several complex matrices in dierent domains, for which we may mention for examples [15].…”