Basics on growth orders of polymonogenic functions

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2015-04-25
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In this paper, we introduce generalizations of the classical growth order and the growth type of analytic functions in the context of polymonogenic functions. Polymonogenic functions are null-solutions of higher integer order iterates of a generalized higher dimensional Cauchy–Riemann operator. One of the main goals is to prove generalizations of the famous Lindelöf–Pringsheim theorem linking explicitly these growth orders and growth types with the Taylor series coefficients in the context of this function class.
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iterated generalized Cauchy–Riemann equations , polymonogenic functions , asymptotic growth behaviour of generalized analytic functions , growth orders , growth type
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