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Quasianalytic ultradifferentiability cannot be tested in lower dimensions

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arxiv 1810.10767 v2 pith:5A4ZIAQP submitted 2018-10-25 math.CA math.FA

Armin Rainer This is my paper · ORCID
classification math.CAmath.FA
keywords dimensionslowerquasianalytictestedultradifferentiabilityanalyticcannotcase
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We show that, in contrast to the real analytic case, quasianalytic ultradifferentiability can never be tested in lower dimensions. Our results are based on a construction due to Jaffe.

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  1. Functions with ultradifferentiable powers

    math.CA 2019-08 accept novelty 7.0 of 10

    Under the moderate growth condition, Joris's power theorem holds for Denjoy-Carleman classes: coprime powers that are C_M force the function itself to be C_M.

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