A Goursat decomposition for polyharmonic functions in Euclidean space
- Author
- Fred Brackx (UGent) , Richard Delanghe (UGent) , Hennie De Schepper (UGent) and Vladimir Soucek
- Organization
- 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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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-3032091
- 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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