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Microlocal analysis in generalized function algebras based on generalized points and generalized directions

Hans Vernaeve (UGent)
(2016) MONATSHEFTE FUR MATHEMATIK. 181. p.205-215
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  • FWO 1.5.138.13N
Abstract
We develop a refined theory of microlocal analysis in the algebra G(Ω) of Colombeau generalized functions. In our approach, the wave front is a set of generalized points in the cotangent bundle of Ω, whereas in the theory developed so far, it is a set of nongeneralized points. We also show consistency between both approaches.
Keywords
Microlocal analysis, Algebras of generalized functions, COEFFICIENTS

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MLA
Vernaeve, Hans. “Microlocal Analysis in Generalized Function Algebras Based on Generalized Points and Generalized Directions.” MONATSHEFTE FUR MATHEMATIK 181 (2016): 205–215. Print.
APA
Vernaeve, H. (2016). Microlocal analysis in generalized function algebras based on generalized points and generalized directions. MONATSHEFTE FUR MATHEMATIK, 181, 205–215.
Chicago author-date
Vernaeve, Hans. 2016. “Microlocal Analysis in Generalized Function Algebras Based on Generalized Points and Generalized Directions.” Monatshefte Fur Mathematik 181: 205–215.
Chicago author-date (all authors)
Vernaeve, Hans. 2016. “Microlocal Analysis in Generalized Function Algebras Based on Generalized Points and Generalized Directions.” Monatshefte Fur Mathematik 181: 205–215.
Vancouver
1.
Vernaeve H. Microlocal analysis in generalized function algebras based on generalized points and generalized directions. MONATSHEFTE FUR MATHEMATIK. 2016;181:205–15.
IEEE
[1]
H. Vernaeve, “Microlocal analysis in generalized function algebras based on generalized points and generalized directions,” MONATSHEFTE FUR MATHEMATIK, vol. 181, pp. 205–215, 2016.
@article{7258152,
  abstract     = {{We develop a refined theory of microlocal analysis in the algebra G(Ω) of Colombeau generalized functions. In our approach, the wave front is a set of generalized points in the cotangent bundle of Ω, whereas in the theory developed so far, it is a set of nongeneralized points. We also show consistency between both approaches.}},
  author       = {{Vernaeve, Hans}},
  issn         = {{0026-9255}},
  journal      = {{MONATSHEFTE FUR MATHEMATIK}},
  keywords     = {{Microlocal analysis,Algebras of generalized functions,COEFFICIENTS}},
  language     = {{eng}},
  pages        = {{205--215}},
  title        = {{Microlocal analysis in generalized function algebras based on generalized points and generalized directions}},
  url          = {{http://dx.doi.org/10.1007/s00605-015-0831-7}},
  volume       = {{181}},
  year         = {{2016}},
}

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