On the Growth Order and Growth Type of Entire Functions of Several Complex Matrices

Abstract

In this paper, we establish an explicit relation between the growth of the maximum modulus and the Taylor coefficients of entire functions in several complex matrix variables (FSCMVs) in hyperspherical regions. e obtained formulas enable us to compute the growth order and the growth type of some higher dimensional generalizations of the exponential, trigonometric, and some special FSCMVs which are analytic in some extended hyperspherical domains. Furthermore, a result concerning linear substitution of the mode of increase of FSCMVs is given.

Some remarks on the generalized order and generalized type of entire functions of several complex matrices

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The main aim of this paper is to introduce the definitions of generalized order and generalized type of the entire function of several complex matrix variables in hyperspherical region and then study some of their properties. By considering the concepts of generalized order and generalized type, we will extend some results of Abul-Ez et al [1].

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Approximation of functions by complex conformable derivative bases in Fréchet spaces

“…Related to order and type of the BP, we refer to previous studies. [46][47][48][49][50][51] Now, we recall the definition of the T 𝜌 -property as given by Abul-Ez and Constales 45 as follows: Definition 9. If 0 < 𝜌 < ∞, then a base is said to have property T 𝜌 in a closed disk D(R), if it represents all entire functions of order less than 𝜌 in D(R).…”

Equivalent Base Expansions in the Space of Cliffordian Functions

“…Several approaches have been pursued in generalizing the theory of classical complex functions. Among these generalizations are the theory of several complex variables and the matrix approach [9][10][11]. The crucial development of the hypercomplex theory derived from higher-dimensional analysis involving Clifford algebra is called Clifford analysis.…”