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December 2019 A nonlinear theory of infrahyperfunctions
Andreas Debrouwere, Hans Vernaeve, Jasson Vindas
Kyoto J. Math. 59(4): 869-895 (December 2019). DOI: 10.1215/21562261-2019-0029

Abstract

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.

Citation

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Andreas Debrouwere. Hans Vernaeve. Jasson Vindas. "A nonlinear theory of infrahyperfunctions." Kyoto J. Math. 59 (4) 869 - 895, December 2019. https://doi.org/10.1215/21562261-2019-0029

Information

Received: 7 April 2017; Accepted: 15 June 2017; Published: December 2019
First available in Project Euclid: 26 September 2019

zbMATH: 07194000
MathSciNet: MR4032202
Digital Object Identifier: 10.1215/21562261-2019-0029

Subjects:
Primary: 46F30
Secondary: 46F15

Rights: Copyright © 2019 Kyoto University

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Vol.59 • No. 4 • December 2019
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