×

The generalized integrals and integral equation in Clifford analysis. (English) Zbl 1221.45002

Summary: With the method of unit resolution, this paper defines the generalized integrals in the sense of M. Spivak on open manifolds for unbounded functions in Clifford analysis, and discusses the solvability and the series expression of the solution to the generalized second kind of integral equation with exchange factors, and gives the error estimate of the approximate computation.

MSC:

45E99 Singular integral equations
30G35 Functions of hypercomplex variables and generalized variables
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Vahlen, K. T., Ü ber Bewegungen und complexe Zahlen, Math Ann, 55, 585-593 (1902) · JFM 33.0721.01
[2] Bracks, F.; Delanghe, R.; Sommen, F., Clifford Analysis (1982), London: Pitman Advanced Publishing Program, London · Zbl 0529.30001
[3] Zhenyuan, Xu, The Riemann Problem for Regular Functions with Values in a Clifford Algebra, Chinese Science Bulletin (in Chinese), 32, 476-477 (1987)
[4] Guochun, Wen, Clifford analysis and elliptic systems, hyperbolic systems of first order equations, 230-237 (1991), (Singapore): World Scientific, (Singapore) · Zbl 0783.30038
[5] Sha, Huang, A Nonlinear Bundary Value Problem for Biregular Functions in Clifford Analysis, Science in China, 39, 1152-1164 (1996) · Zbl 0919.30040
[6] Sha, Huang, A (linear) Nonlinear Boundary Value Problem for Generalized Biregular Fuctions in Clifford Analysis, Acta Mathematical Sinica (in Chinese), 40, 913-920 (1997) · Zbl 0916.30042
[7] Sha, Huang, The Regularization of the Singular Integral Equations on Characteristic Manifold in Clifford Analysis, Mathematica Acta & Cientia, 18, 257-263 (1998) · Zbl 0948.30053
[8] Yuying, Qiao; Sha, Huang; Hongfang, Zhao; Zhenguo, Chen, A nonlinear Boundary Value Problem in Clifford Analysis, Mathematica Acta & Cientia, 16, 284-290 (1996) · Zbl 0902.30028
[9] Yuying, Qiao, A nonlinear boundary value problem with a Haseman shift for biregular function, J. Sys. Sci and Math. Scis., 19, 484-489 (1999) · Zbl 1109.30304
[10] M. Spivak,Calculus on manifolds. Science Publishing House, 1980. · Zbl 0458.26001
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.