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A nonlinear theory of infrahyperfunctions

Andreas Debrouwere (UGent) , Hans Vernaeve (UGent) and Jasson Vindas Diaz (UGent)
(2019) KYOTO JOURNAL OF MATHEMATICS. 59(4). p.869-895
Author
Organization
Abstract
We develop a nonlinear theory for infrahyperfunctions (also referred to as quasianalytic (ultra) distributions by L. Hormander). In the hyperfunction case, our work can be summarized as follows. We construct a differential algebra that contains the space of hyperfunctions as a linear differential subspace and in which the multiplication of real analytic functions coincides with their ordinary product. Moreover, by proving an analogue of Schwartz's impossibility result for hyperfunctions, we show that this embedding is optimal. Our results fully solve an earlier question raised by M. Oberguggenberger.
Keywords
Generalized functions, hyperfunctions, Colombeau algebras, multiplication of infrahyperfunctions, sheaves of infrahyperfunctions, quasianalytic distributions, SPACES, ULTRADISTRIBUTIONS

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MLA
Debrouwere, Andreas, et al. “A Nonlinear Theory of Infrahyperfunctions.” KYOTO JOURNAL OF MATHEMATICS, vol. 59, no. 4, 2019, pp. 869–95, doi:10.1215/21562261-2019-0029.
APA
Debrouwere, A., Vernaeve, H., & Vindas Diaz, J. (2019). A nonlinear theory of infrahyperfunctions. KYOTO JOURNAL OF MATHEMATICS, 59(4), 869–895. https://doi.org/10.1215/21562261-2019-0029
Chicago author-date
Debrouwere, Andreas, Hans Vernaeve, and Jasson Vindas Diaz. 2019. “A Nonlinear Theory of Infrahyperfunctions.” KYOTO JOURNAL OF MATHEMATICS 59 (4): 869–95. https://doi.org/10.1215/21562261-2019-0029.
Chicago author-date (all authors)
Debrouwere, Andreas, Hans Vernaeve, and Jasson Vindas Diaz. 2019. “A Nonlinear Theory of Infrahyperfunctions.” KYOTO JOURNAL OF MATHEMATICS 59 (4): 869–895. doi:10.1215/21562261-2019-0029.
Vancouver
1.
Debrouwere A, Vernaeve H, Vindas Diaz J. A nonlinear theory of infrahyperfunctions. KYOTO JOURNAL OF MATHEMATICS. 2019;59(4):869–95.
IEEE
[1]
A. Debrouwere, H. Vernaeve, and J. Vindas Diaz, “A nonlinear theory of infrahyperfunctions,” KYOTO JOURNAL OF MATHEMATICS, vol. 59, no. 4, pp. 869–895, 2019.
@article{8638964,
  abstract     = {{We develop a nonlinear theory for infrahyperfunctions (also referred to as quasianalytic (ultra) distributions by L. Hormander). In the hyperfunction case, our work can be summarized as follows. We construct a differential algebra that contains the space of hyperfunctions as a linear differential subspace and in which the multiplication of real analytic functions coincides with their ordinary product. Moreover, by proving an analogue of Schwartz's impossibility result for hyperfunctions, we show that this embedding is optimal. Our results fully solve an earlier question raised by M. Oberguggenberger.}},
  author       = {{Debrouwere, Andreas and Vernaeve, Hans and Vindas Diaz, Jasson}},
  issn         = {{2156-2261}},
  journal      = {{KYOTO JOURNAL OF MATHEMATICS}},
  keywords     = {{Generalized functions,hyperfunctions,Colombeau algebras,multiplication of infrahyperfunctions,sheaves of infrahyperfunctions,quasianalytic distributions,SPACES,ULTRADISTRIBUTIONS}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{869--895}},
  title        = {{A nonlinear theory of infrahyperfunctions}},
  url          = {{http://doi.org/10.1215/21562261-2019-0029}},
  volume       = {{59}},
  year         = {{2019}},
}
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