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SPHERICAL MEANS, DISTRIBUTIONS AND CONVOLUTION OPERATORS IN CLIFFORD ANALYSIS 被引量:5

SPHERICAL MEANS, DISTRIBUTIONS AND CONVOLUTION OPERATORS IN CLIFFORD ANALYSIS
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摘要 New higher dimensional distributions are introduced in the framework of Clifford analysis.They complete the picture already established in previous work, offering unity and structuralclarity. Amongst them are the building blocks of the principal value distribution, involvingspherical harmonics, considered by Horvath and Stein.
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2003年第2期133-146,共14页 数学年刊(B辑英文版)
关键词 Spherical means DISTRIBUTIONS Convolution operators Clifford analysis 卷积算子 球面均值 分布 Clifford分析 Clifford代数 正则函数 复变量
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  • 1Brackx, F., Delanghe, R. & Sommen, F., Clifford analysis, Pitman Publ., 1982.
  • 2Brackx, F., Delanghe, R. & Sommen, F., Spherical means and distributions in Clifford analysis, Proceedings of the Macao Conference on Clifford Analysis, Birkhauser, 2002.
  • 3Delanghe, R., Some remarks on the principal value kernel, Complex Variables: Theory and Application,47(2002), 653-662.
  • 4Delanghe, R., Sommen, F. & Soucek, V., Clifford algebra and spinor-valued functions, Kluwer Academic Publ., 1992.
  • 5Gelfand, I. M. & Shilov, G. E., Generalized functions, Vol. 1, Academic Press, 1964.
  • 6Gilbert, J. & Murray, M., Clifford algebra and Dirac operators in harmonic analysis, Cambridge Univ.Press, 1991.
  • 7Horvath, J., Singular integral operators and spherical harmonics, Trans. Amer. Math. Soc., 82(1950),52-63.
  • 8Schwartz, L., Theorie des distributions, Hermann, 1966.
  • 9Stein, E. & WeiB, G., Introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, 1971.
  • 10Sommen, F., Spin groups and spherical means, in Clifford Algebras and Their Applications in Mathematical Physics, J. S. R. Chisholm and A. K. Common (eds.), Nato ASI Series, D. Reidel Publ. Co.,1985.

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