The Growth of Generalized Hadamard Product of Entire Axially Monogenic Functions

Abstract

In this article, we estimated upper bounds for the growth order and growth type of generalized Hadamard product entire axially monogenic functions. Also, some results concerning the linear substitution are discussed. The obtained results are the natural generalizations of those given in complex setting of one variable to higher dimensions of more than four.

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).…”

“…3. In previous studies, 13,15,19,[45][46][47][48]51,54,59 the convergence properties in different regions of associated BP (such as inverse base, product base, transpose base, transposed inverse base, square root base, similar base, Hadamard product base ) were studied. Is the CCFDB and CCFIB of these bases convergent in the same regions?…”

“…If possible, we can generalize the theorems proven in Section 5 of this paper in several complex variables. In this case, we expect the convergence regions to be spherical regions or polycylinderical regions, or elliptical regions. In previous studies, 13,15,19,45–48,51,54,59 the convergence properties in different regions of associated BP (such as inverse base, product base, transpose base, transposed inverse base, square root base, similar base, Hadamard product base ) were studied. Is the CCFDB and CCFIB of these bases convergent in the same regions? In the future it is possible to study the convergent properties of new bases of polynomials in different regions (e.g., Laguerre, Lagender, Hermit, and Gontcharoff polynomials).…”