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Hypermonogenic solutions and plane waves of the Dirac operator in \(\mathbb{R}^p \times \mathbb{R}^q\). (English) Zbl 1428.30051

Summary: In this paper, we first define hypermonogenic solutions of the Dirac operator in \(\mathbb{R}^p \times \mathbb{R}^q\) and study some basic properties, e.g., obtaining a Cauchy integral formula in the unit hemisphere. Hypermonogenic solutions form a natural function class in classical Clifford analysis. After that, we define the corresponding hypermonogenic plane wave solutions and deduce explicit methods to compute these functions.

MSC:

30G35 Functions of hypercomplex variables and generalized variables
35Q41 Time-dependent Schrödinger equations and Dirac equations
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References:

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