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Generalized Almansi Expansions in Superspace

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Abstract

In this paper, we first study an expansion for the operators

$$\begin{aligned} (\partial _{x}-\lambda )^{k}, \end{aligned}$$

where \(\partial _{x}\) is the Dirac operator in superspace and \(\lambda \) is a complex number. Then we investigate expansions for polynomial Dirac operators in superspace. These expansions are regarded as generalized Almansi expansions in superspace. As an application of the expansions, the modified Riquier problem in superspace is considered.

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Authors and Affiliations

  1. College of Science, Hebei University of Engineering, Handan, 056038, China

    Hongfen Yuan

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  1. Hongfen Yuan
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Correspondence to Hongfen Yuan.

Additional information

Communicated by Klaus Gürlebeck.

Research supported by the TianYuan Special Funds of the National Natural Science Foundation of China under Grant No. 11426082, and Project of Handan Municipal Science and Technology Bureau under Grant No. 1534201097-10.

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Yuan, H. Generalized Almansi Expansions in Superspace. Comput. Methods Funct. Theory 16, 515–527 (2016). https://doi.org/10.1007/s40315-015-0153-8

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  • DOI: https://doi.org/10.1007/s40315-015-0153-8

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