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Modulus of Smoothness and Approximation Theorems in Clifford Analysis

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Abstract

This paper uses some basic results on Clifford analysis introduced by E. Hitzer, to study some problems in the theory of approximation of functions in the space of square integral functions in the Clifford algebra. The equivalence between the moduli of smoothness of all orders constructed by the Steklov function and the K-functionals constructed from the Sobolev-type space is proved. A consequence of this equivalence theorem is given at the end of this work.

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Acknowledgements

The authors will be grateful to the referees for the useful comments and suggestions in improving the presentation of the paper.

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  1. Laboratory of Fundamental and Applied Mathematics, Department of Mathematics, Faculty of Sciences Aïn Chock, University Hassan II, Casablanca, Morocco

    Othman Tyr

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  1. Othman Tyr
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Communicated by Uwe Kahler.

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Tyr, O. Modulus of Smoothness and Approximation Theorems in Clifford Analysis. Complex Anal. Oper. Theory 18, 3 (2024). https://doi.org/10.1007/s11785-023-01447-4

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