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Keywords:

generalized cauchy-riemann system, entire monogenic functions, growth orders, asymptotic behavior of the maximum modulus, generalized trigonometric functions, monogenic functions, series, order, Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, generalized Cauchy-Riemann system, MONOGENIC FUNCTIONS, SERIES, ORDER, 0101 Pure Mathematics, 0102 Applied Mathematics, 0906 Electrical and Electronic Engineering, General Mathematics, 4901 Applied mathematics, 4903 Numerical and computational mathematics, 4904 Pure mathematics

Abstract:

In this paper we establish an explicit relation between the growth of the maximum modulus and the Taylor coefficients of the entire solutions to the higher-dimensional Cauchy-Riemann system in R^{n+1}. This allows us to determine the exact value for the growth order of the maximum modulus for all entire monogenic functions without knowing the precise value for the maximum modulus. Furthermore, it enables us to construct easily examples of entire monogenic functions that exhibit growth behavior of order p for any real value 0 <= rho <= infinity. (c) 2006 Elsevier Inc. All rights reserved.