Kyoto Journal of Mathematics

A nonlinear theory of infrahyperfunctions

Andreas Debrouwere, Hans Vernaeve, and Jasson Vindas

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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.

Article information

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

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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]

generalized functions hyperfunctions Colombeau algebras multiplication of infrahyperfunctions sheaves of infrahyperfunctions quasianalytic distributions


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.

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