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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66531There 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.17 pages, LaTeX2eComplex Variables30G35, 32V05On boundary values for rectifiable curves of a generalization of the Cauchy-type integral related to the Helmholtz operator in $R^2$text