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Optimal embeddings of ultradistributions into differential algebras

Andreas Debrouwere (UGent) , Hans Vernaeve (UGent) and Jasson Vindas Diaz (UGent)
(2018) MONATSHEFTE FUR MATHEMATIK. 186(3). p.407-438
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Abstract
We construct embeddings of spaces of non-quasianalytic ultradistributions into differential algebras enjoying optimal properties in view of a Schwartz type impossibility result, also shown in this article. We develop microlocal analysis in these algebras consistent with the microlocal analysis in the corresponding spaces of ultradistributions.
Keywords
Generalized functions, Colombeau algebras, Multiplication of ultradistributions, Wave front sets, Ultradifferentiable functions, Denjoy-Carleman classes, GENERALIZED-FUNCTIONS, MICROLOCAL ANALYSIS, REGULARITY PROPERTIES, DISTRIBUTIONS, OPERATORS, SPACES, COEFFICIENTS, SETS

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Citation

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

Chicago
Debrouwere, Andreas, Hans Vernaeve, and Jasson Vindas Diaz. 2018. “Optimal Embeddings of Ultradistributions into Differential Algebras.” Monatshefte Fur Mathematik 186 (3): 407–438.
APA
Debrouwere, A., Vernaeve, H., & Vindas Diaz, J. (2018). Optimal embeddings of ultradistributions into differential algebras. MONATSHEFTE FUR MATHEMATIK, 186(3), 407–438.
Vancouver
1.
Debrouwere A, Vernaeve H, Vindas Diaz J. Optimal embeddings of ultradistributions into differential algebras. MONATSHEFTE FUR MATHEMATIK. 2018;186(3):407–38.
MLA
Debrouwere, Andreas, Hans Vernaeve, and Jasson Vindas Diaz. “Optimal Embeddings of Ultradistributions into Differential Algebras.” MONATSHEFTE FUR MATHEMATIK 186.3 (2018): 407–438. Print.
@article{8524429,
  abstract     = {We construct embeddings of spaces of non-quasianalytic ultradistributions into differential algebras enjoying optimal properties in view of a Schwartz type impossibility result, also shown in this article. We develop microlocal analysis in these algebras consistent with the microlocal analysis in the corresponding spaces of ultradistributions.},
  author       = {Debrouwere, Andreas and Vernaeve, Hans and Vindas Diaz, Jasson},
  issn         = {0026-9255},
  journal      = {MONATSHEFTE FUR MATHEMATIK},
  keywords     = {Generalized functions,Colombeau algebras,Multiplication of ultradistributions,Wave front sets,Ultradifferentiable functions,Denjoy-Carleman classes,GENERALIZED-FUNCTIONS,MICROLOCAL ANALYSIS,REGULARITY PROPERTIES,DISTRIBUTIONS,OPERATORS,SPACES,COEFFICIENTS,SETS},
  language     = {eng},
  number       = {3},
  pages        = {407--438},
  title        = {Optimal embeddings of ultradistributions into differential algebras},
  url          = {http://dx.doi.org/10.1007/s00605-017-1066-6},
  volume       = {186},
  year         = {2018},
}

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