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On boundary values for rectifiable curves of a generalization of the Cauchy-type integral related to the Helmholtz operator in $R^2$

Oleg F. Gerus·Michael Shapiro
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Abstract

There are considered vector fields and quaternionic $α$-hyperholomorphic functions in a domain of $R^2$ which generalize the notion of solenoidal and irrotational vector fields. There are established sufficient conditions for the corresponding Cauchy-type integral along a closed Jordan rectifiable curve to be continuously extended onto the closure of a domain. The Sokhotski-Plemelj-type formulas are proved as well.

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Oleg F. Gerus, Michael Shapiro. 2003-02-14. On boundary values for rectifiable curves of a generalization of the Cauchy-type integral related to the Helmholtz operator in $R^2$. https://arxiv.org/abs/math/0302176

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