Abstract
As a case of the Laplacian, the Helmholtz operator can be factorized using perturbed Dirac operators. In this article, we prove Schwarz lemmas for solutions of perturbed Dirac operators in vector space $$\mathbb {R}^{3}$$ by the integral representation formulas. As an immediate consequence of the Schwarz lemma, one has Liouville’s theorem for monogenic functions in Clifford analysis.
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