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Clifford Analysis on the Sphere

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Part of the book series: Fundamental Theories of Physics ((FTPH,volume 94))

Abstract

In this paper we give some basic integral formulas related to spherical monogenics of complex degree. These monogenics, locally defined on the sphere S m−1, are eigenfunctions of the Γ-operator corresponding to complex eigenvalues and generalise the classical spherical monogenics.

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References

  1. Brackx F., Delanghe R. and Sommen F. (1982) Clifford Analysis, Pitman, London.

    MATH  Google Scholar 

  2. Deans S. R. (1979) Gegenbauer transforms via the Radon transform, SIAM J. Math. Anal. 10, 577–585.

    Article  MathSciNet  MATH  Google Scholar 

  3. Durand L., Fishbane P. M. and Simmons L. M., Jr. (1976) Expansion formulas and addition theorems for Gegenbauer functions, J. Math. Phys. 17, 1933–1948.

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  4. Delanghe R., Sommen F. and Souček V. (1992) Clifford algebra and spinor valued functions: a function theory for the Dirac operator, Kluwer, Dordrecht.

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  5. Erdélyi A., Magnus W., Oberhettinger F. and Tricomi F. (1953) Higher Transcendental functions, Mc Graw-Hill, New York

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  6. Ryan J. Dirac operators on spheres and hyperbolae, preprint.

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  7. Sommen F. (1981) Spherical monogenic functions and analytic functionals on the unit sphere, Tokyo Journal of Mathematics 4, 427–456.

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  8. Sommen F. and Van Lancker P. Homogeneous monogenic functions in Euclidean space, in preparation.

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  9. (1996) Clifford Analysis on the sphere, Ph. D.-thesis, Ghent.

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© 1998 Springer Science+Business Media Dordrecht

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Van Lancker, P. (1998). Clifford Analysis on the Sphere. In: Dietrich, V., Habetha, K., Jank, G. (eds) Clifford Algebras and Their Application in Mathematical Physics. Fundamental Theories of Physics, vol 94. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5036-1_16

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  • DOI: https://doi.org/10.1007/978-94-011-5036-1_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6114-8

  • Online ISBN: 978-94-011-5036-1

  • eBook Packages: Springer Book Archive

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