Abstract
We give an overview of Riemann-Hilbert problems and related topics in Clifford analysis as generalizations of the classical complex problem and its basic properties.
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References
Alexandroff, P., Hopf, H.: Topology, Springer Verlag, Berlin, 1935.
Bernstein, S.: 1996, ‘On the left linear Riemann problem in Clifford analysis’, Bull. Belg. Math.Soc., Simon Stevin Vol. no. 2, pp. 557–576
Bernstein, S.: 1999, ‘The Quaternionic Riemann problem’, in: Function Spaces, Proc. of the Third Conference on Function Spaces, Edwardsville, 1998, ed. by K. Jarosz, Contemporary Mathematics Vol. no. 232, pp. 69–84
Bernstein, S.: 1999, ‘Nonlinear Singular Integral Equations Involving the Hilbert Transform in Clifford Analysis’, Zeitschrift für Analysis und ihre Anwendungen Vol. no. 18(2), pp. 379–392
Brackx, F., Delanghe, R. and Sommen, F.: Clifford Analysis. Research Notes in Mathematics 76, Pitman Adv. Publ. Program, 1982.
Delanghe, R., Sommen, F. and Souček, V.: Clifford algebra and Spinor-valued functions. Kluwer Acad. Publ., Dordrecht, Boston, London, 1992
Gilbert, J. E. and Murray, M. A. M.: Clifford Algebras and Dirac Operators in harmonic Analysis. Cambridge studies in adv. math. Vol. 26, Cambridge University Press, Cambridge 1991
Gürlebeck, K. and Sprößig, W.: Quaternionic and Clifford calculus for Engineers and Physicists. Wiley & Sons Publ., 1997
Habetha, K.: 1986, ‘Eine Definition des Kronecker Indexes in ℝn+1 mit Hilfe der Clifford Analysis’, Zeitschrift für Analysis und ihre Anwendungen Vol. no. 5(2), pp.133–137
Gakhov, F. D.: Boundary Value Problems. Dover Publ. Inc., New York, 1990
Hestenes, D. and Sobczyk, G.: Clifford algebra to Geometric Calculus. D. Reidel Publ. Comp., Dordrecht, Holland, 1985
Mcintosh, A., Li, C. and Semmes, S.: 1992, ‘Convolution singular integrals on Lipschitz surfaces’, Journal of the American Mathematical Society Vol. no. 5, pp.455–481
Muskhelishvili, N.L: Singular Integral Equations. Dover Publ., Inc., New York, 1992
Shapiro, M.V. and Vasilevski, N.L.: 1995, ‘Quaternionic Ψ-holomorphic functions, singular integral operators and boundary value problems, I, II’ Complex Variables, Theory and Applications Vol. no. 27, pp. 14–46 and 67-96
Stern, I.: ‘Boundary value problems for generalized Cauchy-Riemann systems in the space.’ In: Kühnau, R. and Tutschke, W. (eds.), Boundary value and initial value problems in complex analysis. Pitman Res. Notes in Math., pp.159–183
Sudbery, A.: 1979, ‘Quaternionic analysis’, Math. Proc. Cambr. Phil. Soc. Vol. no. 85, pp.199–225
Sommen, F.: 1984, ‘Monogenic differential forms and homology theory.’ Proc. Royal Irish Academy Vol. no. 84 A, pp.87–109
Vekua, I.N.: Generalizes analytic functions. Nauka, Moskow, 1959, (Russian)
Wegert, E.: Nonlinear Boundary Value Problems for Holomorphic Functions and Singular Integral Equations. Mathematical Research Vol. 65, Akademie Verlag Berlin, 1992
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Bernstein, S. (2001). Riemann-Hilbert Problems in Clifford Analysis. In: Brackx, F., Chisholm, J.S.R., Souček, V. (eds) Clifford Analysis and Its Applications. NATO Science Series, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0862-4_1
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DOI: https://doi.org/10.1007/978-94-010-0862-4_1
Publisher Name: Springer, Dordrecht
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