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Optimal embeddings of distributions into algebras

Hans Vernaeve (UGent)
Author
Organization
Abstract
Let Omega be a convex, open subset of R-n and let D'(Omega) be the space of distributions on Omega. It is shown that there exist linear embeddings of V(Omega) into a differential algebra that commute with partial derivatives and that embed C-infinity(Omega) as a subalgebra. This embedding appears to be the first one after Colombeau's to possess these properties. We show that many nonlinear operations on distributions can be defined that are not definable in the Colombeau setting.
Keywords
distributions, generalized functions, embeddings, injective modules, Colombeau

Citation

Please use this url to cite or link to this publication:

MLA
Vernaeve, Hans. “Optimal Embeddings of Distributions into Algebras.” PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY 46.2 (2003): 373–378. Print.
APA
Vernaeve, H. (2003). Optimal embeddings of distributions into algebras. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 46(2), 373–378.
Chicago author-date
Vernaeve, Hans. 2003. “Optimal Embeddings of Distributions into Algebras.” Proceedings of the Edinburgh Mathematical Society 46 (2): 373–378.
Chicago author-date (all authors)
Vernaeve, Hans. 2003. “Optimal Embeddings of Distributions into Algebras.” Proceedings of the Edinburgh Mathematical Society 46 (2): 373–378.
Vancouver
1.
Vernaeve H. Optimal embeddings of distributions into algebras. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY. 2003;46(2):373–8.
IEEE
[1]
H. Vernaeve, “Optimal embeddings of distributions into algebras,” PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, vol. 46, no. 2, pp. 373–378, 2003.
@article{415465,
  abstract     = {Let Omega be a convex, open subset of R-n and let D'(Omega) be the space of distributions on Omega. It is shown that there exist linear embeddings of V(Omega) into a differential algebra that commute with partial derivatives and that embed C-infinity(Omega) as a subalgebra. This embedding appears to be the first one after Colombeau's to possess these properties. We show that many nonlinear operations on distributions can be defined that are not definable in the Colombeau setting.},
  author       = {Vernaeve, Hans},
  issn         = {0013-0915},
  journal      = {PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY},
  keywords     = {distributions,generalized functions,embeddings,injective modules,Colombeau},
  language     = {eng},
  number       = {2},
  pages        = {373--378},
  title        = {Optimal embeddings of distributions into algebras},
  url          = {http://dx.doi.org/10.1017/S0013091500001188},
  volume       = {46},
  year         = {2003},
}

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