2019
DOI: 10.1215/21562261-2019-0029
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A nonlinear theory of infrahyperfunctions

Abstract: We develop a non-linear theory for infrahyperfunctions (also known as quasianalytic (ultra)distributions [25]). 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. … Show more

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Cited by 4 publications
(6 citation statements)
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“…From now on we assume that M p satisfies (M.0), (M.1), (M.2) , and (QA). Our next considerations are in terms of sheaves of quasianalytic ultradistributions, we briefly discuss their properties following the approach from [5,10] (cf. [17] for hyperfunctions).…”
Section: Rotation Invariant Ultradistributionsmentioning
confidence: 99%
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“…From now on we assume that M p satisfies (M.0), (M.1), (M.2) , and (QA). Our next considerations are in terms of sheaves of quasianalytic ultradistributions, we briefly discuss their properties following the approach from [5,10] (cf. [17] for hyperfunctions).…”
Section: Rotation Invariant Ultradistributionsmentioning
confidence: 99%
“…3.5], that is, for any * -quasianalytic functional there is a smallest * -carrier, say supp E * f , and one has supp A f = supp E * f . Hörmander only treats the Roumieu case in [10], but his proof can be modified to show the corresponding statement for the Beurling case [5,8].…”
Section: Rotation Invariant Ultradistributionsmentioning
confidence: 99%
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“…If one further restricts to nets of real valued constant functions, the resulting quotient algebra is R. The space of generalized functions G(Ω) then becomes a module over the ring C. We refer to [2,4,9] more details on Colombeau algebras. See also [5,6] for non-linear theories of ultradistributions and hyperfunctions.…”
Section: 2mentioning
confidence: 99%
“…We shall also give sufficient conditions on a locally convex space F such that the Cousin problem is solvable in spaces of F -valued quasianalytic functions. We mention that in a forthcoming paper [9] the authors will apply the vectorvalued results from this article to construct sheaves of differential algebras in which the spaces of infrahyperfunctions of class {M p } [16] are embedded in such a way that the ordinary multiplication of ultradifferentiable functions of class {M p } is preserved.…”
Section: Introductionmentioning
confidence: 99%