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The Hilbert Transform on the Unit Sphere in R^m

Fred Brackx (UGent) and Hennie De Schepper (UGent)
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Organization
Abstract
As an intrinsically multidimensional function theory, Clifford analysis offers a framework which is particularly suited for the integrated treatment of higher-dimensional phenomena. In this paper a detailed account is given of results connected to the Hilbert transform on the unit sphere in Euclidean space and some of its related concepts, such as Hardy spaces and the Cauchy integral, in a Clifford analysis context.

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Chicago
Brackx, Fred, and Hennie De Schepper. 2009. “The Hilbert Transform on the Unit Sphere in R^m.” In Trends in Mathematics, ed. Irene Sabadini, Michael Shapiro, and Franciscus Sommen, 11–36. Basel-Boston-Berlin: Birkhäuser Verlag.
APA
Brackx, Fred, & De Schepper, H. (2009). The Hilbert Transform on the Unit Sphere in R^m. In Irene Sabadini, M. Shapiro, & F. Sommen (Eds.), Trends in Mathematics (pp. 11–36). Presented at the 6th Congress of the International Society for Analysis its Applications and Computation, Basel-Boston-Berlin: Birkhäuser Verlag.
Vancouver
1.
Brackx F, De Schepper H. The Hilbert Transform on the Unit Sphere in R^m. In: Sabadini I, Shapiro M, Sommen F, editors. Trends in Mathematics. Basel-Boston-Berlin: Birkhäuser Verlag; 2009. p. 11–36.
MLA
Brackx, Fred, and Hennie De Schepper. “The Hilbert Transform on the Unit Sphere in R^m.” Trends in Mathematics. Ed. Irene Sabadini, Michael Shapiro, & Franciscus Sommen. Basel-Boston-Berlin: Birkhäuser Verlag, 2009. 11–36. Print.
@inproceedings{681648,
  abstract     = {As an intrinsically multidimensional function theory, Clifford analysis offers a framework which is particularly suited for the integrated treatment of higher-dimensional phenomena. In this paper a detailed account is given of results connected to the Hilbert transform on the unit sphere in Euclidean space and some of its related concepts, such as Hardy spaces and the Cauchy integral, in a Clifford analysis context.},
  author       = {Brackx, Fred and De Schepper, Hennie},
  booktitle    = {Trends in Mathematics},
  editor       = {Sabadini, Irene and Shapiro, Michael and Sommen, Franciscus},
  isbn         = {978-3-7643-9892-7},
  language     = {eng},
  location     = {Ankara},
  pages        = {11--36},
  publisher    = {Birkh{\"a}user Verlag},
  title        = {The Hilbert Transform on the Unit Sphere in R\^{ }m},
  year         = {2009},
}

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