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Certain Bases of Polynomials Associated with Entire Functions in Clifford Analysis

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Abstract

The theory of polynomial bases in one complex variable, as given by Whittaker and Cannon, was extended partially to the scope of Clifford analysis, where many results have been handled from different aspects. The emphasis of this paper is on introducing a certain type of bases of axially monogenic polynomials generated by the maximum modulus base. Determining the convergence properties of such bases is closely related to the growth behavior of the associated entire axially monogenic functions. We start by investigating the presented bases of monogenic polynomials associated with entire axially monogenic functions in the way we are going to indicate. Then, we show how this leads us to certain relations involving maximum moduli of an entire axially monogenic function on a sequence of balls with increasing radii. In this concern, we point out that Hadamard’s three hyper-balls theorem can be employed to justify some of our results. The significance of this study is due to the variety of the results, which are not normally expected.

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Acknowledgements

The author appreciates the support provided by the Deanship of Scientific Research at King Khalid University, Saudi Arabia through the General Research Program under grant GRP-29-42. The author is also grateful to the editor and referees for their insightful comments and valuable suggestions which definitely improve this work.

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  1. Mathematics Department, College of Science, King Khalid University, Abha, Saudi Arabia

    Mohra Zayed

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  1. Mohra Zayed
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Correspondence to Mohra Zayed.

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Communicated by Wolfgang Sprössig

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Zayed, M. Certain Bases of Polynomials Associated with Entire Functions in Clifford Analysis. Adv. Appl. Clifford Algebras 31, 28 (2021). https://doi.org/10.1007/s00006-021-01128-5

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