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Some properties of a Cauchy type integral in a three-dimensional commutative algebra with one-dimensional radical. (English) Zbl 1422.30073

Summary: In the paper we consider a certain analog of the Cauchy type integral taking values in a three-dimensional commutative algebra over the field of complex numbers with one-dimensional radical. We have established sufficient conditions for the existence of limiting values for such an integral. It is also shown that analogues of Sokhotskii-Plemelj formulas hold.

MSC:

30G35 Functions of hypercomplex variables and generalized variables
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
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