# zbMATH — the first resource for mathematics

Cauchy integral formula and Plemelj formula of bihypermonogenic functions in real Clifford analysis. (English) Zbl 1177.30061
Summary: In the first part of this article, we give the definition of bihypermonogenic functions in Clifford analysis. Using the idea of quasi-permutation, introduced by S. Huang [J. Syst. Sci. Math. Sci. 18, No.3, 380–384 (1998; Zbl 0928.30030)], we state an equivalent condition for bihypermonogenicity. In the second part, we discuss the Cauchy integral formula and Plemelj formula for the bihypermonogenic functions in real Clifford analysis.
Reviewer: Reviewer (Berlin)

##### MSC:
 30G30 Other generalizations of analytic functions (including abstract-valued functions) 34B05 Linear boundary value problems for ordinary differential equations 31B10 Integral representations, integral operators, integral equations methods in higher dimensions
Full Text:
##### References:
 [1] Delanghe R, Clifford Algebra and Spinor-Valued Functions (1992) [2] Franks E, Bounded Monogenic Functions on Unbounded Domains. Contemporary Mathematics (1998) · Zbl 0890.30034 [3] Huang S, Sci. China, Ser. A 39 pp 1152– (1996) [4] Qiao YY, J. Sys. Sci. Math. Sci 19 pp 484– (1999) [5] Wen, GC. 1991.Clifford analysis and Elliptic System, Hyperbolic Systems of First Order Equations, 230–237. Singapore: World Scientific. [6] DOI: 10.1007/BF03042221 · Zbl 1221.30109 · doi:10.1007/BF03042221 [7] DOI: 10.1080/17476939208814508 · Zbl 0758.30037 · doi:10.1080/17476939208814508 [8] Leutwiler H, Complex Variables 20 pp 19– (1992) [9] Eriksson S-L, Clifford An. 2 pp 286– (2000) [10] Eriksson S-L, in Trends in Mathematics: Advances in Analysis and Geometry pp 97– (2004) · doi:10.1007/978-3-0348-7838-8_5 [11] Eriksson S-L, Bull. Belgian Math. Soc. 11 pp 705– (2004) [12] DOI: 10.1007/BF02884717 · Zbl 1129.30323 · doi:10.1007/BF02884717 [13] Zhang ZX, Chin. Ann. Math. 23 pp 421– (2001) [14] Zhang ZX, Acta Math. Sci. 23 pp 692– (2003) [15] Huang S, Real and Complex Clifford Analysis (2005) [16] Huang S, J. Sys. Sci. and Math. Sci 18 pp 380– (1998) [17] Gilbert RP, A Function Theoretic Approach (1983)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.