A kind of Riemann boundary value problems for pseudo-harmonic functions in Clifford analysis. (English) Zbl 1288.30052
Summary: Some properties of singular integrals with parameter are discussed. We prove a Liouville-type theorem for pseudo-monogenic functions and pseudo-harmonic functions. With the help of them, \(\mathbf{R}_{-1}\) Riemann boundary value problems for pseudo-monogenic functions and pseudo-harmonic functions with values in a Clifford algebra \({Cl}({V}_{3.3})\) are investigated in the classical sense and their explicit representation of solutions are obtained.
MSC:
| 30G35 | Functions of hypercomplex variables and generalized variables |
Keywords:
Clifford analysis; Riemann boundary value problem; pseudo-harmonic functions; pseudo-monogenic functionsReferences:
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