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arXiv · 2502.20740

Generalized {\Pi}-operator in the theory of slice monogenic functions and applications

Ziyi Sun·Chao Ding
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Abstract

The {\Pi}-operator plays an important role in complex analysis, especially in the theory of generalized analytic functions in the sense of Vekua. In this paper, we introduce a generalized {\Pi}-operator in the theory of slice monogenic functions, and some mapping properties of the generalized {\Pi}-operator are also introduced. Further, a left and right inverse and the adjoint operator of the generalized {\Pi}-operator are given. As an application, we introduce a slice Beltrami equation, which reduces to the classical complex Beltrami equation when the dimension is 2. We show details that the norm estimate of the generalized {\Pi}-operator can determine the existence of solutions of the slice Beltrami equation.

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Ziyi Sun, Chao Ding. 2025-02-28. Generalized {\Pi}-operator in the theory of slice monogenic functions and applications. https://arxiv.org/abs/2502.20740

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