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A Goursat decomposition for polyharmonic functions in Euclidean space

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Abstract
The Goursat representation formula in the complex plane, expressing a real–valued biharmonic function in terms of two holomorphic functions and their anti–holomorphic complex conjugates, is generalized to Euclidean space, expressing a real–valued polyharmonic function of order p in terms of p so–called monogenic functions of Clifford analysis.
Keywords
polyharmonic functions, Goursat decomposition

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Chicago
Brackx, Fred, Richard Delanghe, Hennie De Schepper, and Vladimir Soucek. 2012. “A Goursat Decomposition for Polyharmonic Functions in Euclidean Space.” Advances in Applied Clifford Algebras 22 (3): 563–575.
APA
Brackx, Fred, Delanghe, R., De Schepper, H., & Soucek, V. (2012). A Goursat decomposition for polyharmonic functions in Euclidean space. ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 22(3), 563–575.
Vancouver
1.
Brackx F, Delanghe R, De Schepper H, Soucek V. A Goursat decomposition for polyharmonic functions in Euclidean space. ADVANCES IN APPLIED CLIFFORD ALGEBRAS. 2012;22(3):563–75.
MLA
Brackx, Fred, Richard Delanghe, Hennie De Schepper, et al. “A Goursat Decomposition for Polyharmonic Functions in Euclidean Space.” ADVANCES IN APPLIED CLIFFORD ALGEBRAS 22.3 (2012): 563–575. Print.
@article{3032091,
  abstract     = {The Goursat representation formula in the complex plane, expressing a real--valued biharmonic function in terms of two holomorphic functions and their anti--holomorphic complex conjugates, is generalized to Euclidean space, expressing a real--valued polyharmonic function of order p in terms of p so--called monogenic functions of Clifford analysis.},
  author       = {Brackx, Fred and Delanghe, Richard and De Schepper, Hennie and Soucek, Vladimir},
  issn         = {0188-7009},
  journal      = {ADVANCES IN APPLIED CLIFFORD ALGEBRAS},
  keyword      = {polyharmonic functions,Goursat decomposition},
  language     = {eng},
  number       = {3},
  pages        = {563--575},
  title        = {A Goursat decomposition for polyharmonic functions in Euclidean space},
  url          = {http://dx.doi.org/10.1007/s00006-012-0348-2},
  volume       = {22},
  year         = {2012},
}

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