Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 59, Number 4 (2019), 869-895.
A nonlinear theory of infrahyperfunctions
We develop a nonlinear theory for infrahyperfunctions (also referred to as quasianalytic (ultra)distributions by L. Hörmander). 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.
Kyoto J. Math., Volume 59, Number 4 (2019), 869-895.
Received: 7 April 2017
Accepted: 15 June 2017
First available in Project Euclid: 26 September 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Primary: 46F30: Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
Secondary: 46F15: Hyperfunctions, analytic functionals [See also 32A25, 32A45, 32C35, 58J15]
Debrouwere, Andreas; Vernaeve, Hans; Vindas, Jasson. A nonlinear theory of infrahyperfunctions. Kyoto J. Math. 59 (2019), no. 4, 869--895. doi:10.1215/21562261-2019-0029. https://projecteuclid.org/euclid.kjm/1569484831