On the Growth Order and Growth Type of Entire Functions of Several Complex Matrices
Mahmoud Abul-Ez, Hala Abd-Elmageed, Muajebah Hidan, Mohamed Abdalla · Journal of Function Spaces · 2020
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. The 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.