Plemelj formula of inframonogenic functions and their boundary value problems. (English) Zbl 1520.30072
Summary: In this paper, firstly, we study the continuity of Cauchy-type integral operator \(C_\Gamma^{\text{infra}}\) associated with inframonogenic functions and give the Plemelj formula. Secondly, we prove the properties of the Teodorescu operator related to the inframonogenic functions, including its boundness, continuity and differentiability. Finally, we give the related integral representation of Riemann boundary value problems for inframonogenic functions and generalized inframonogenic functions.
MSC:
| 30G35 | Functions of hypercomplex variables and generalized variables |
| 30E20 | Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane |
| 30E25 | Boundary value problems in the complex plane |
Keywords:
inframonogenic functions; Cauchy-type integral operator; Teodorescu operator; Riemann boundary value problemReferences:
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