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Generalized Growth Orders for Polymonogenic Functions and Related Inequalities

de Almeida, Regina; Kraußhar, R.S.

Complex Analysis and Operator Theory, 10(2) (2016), 233–250

In this paper we introduce generalized growth orders and growth types in the sense of Shah and Seremeta in the context of polymonogenic functions. They provide a refinement of previously introduced growth orders in the study of the asymptotic growth behavior of functions satisfying higher dimensional Cauchy–Riemann type equations. We prove a number of insight giving inequalities and manage to extend some basic results that were recently proved for the context of the usual first order Cauchy–Riemann system in Clifford analysis.