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On the characterization of p-adic Colombeau-Egorov generalized functions by their point values

Eberhard Mayerhofer
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Abstract

We show that contrary to recent papers by S. Albeverio, A. Yu. Khrennikov and V. Shelkovich, point values do not determine elements of the so-called p-adic Colombeau-Egorov algebra uniquely. We further show in a more general way that for an Egorov algebra of generalized functions on a locally compact ultrametric space (M,d) taking values in a non-trivial ring, a point value characterization holds if and only if (M,d) is discrete. Finally, following an idea due to M. Kunzinger and M. Oberguggenberger, a generalized point value characterization of such an Egorov algebra is given. Elements of the latter are constructed which differ from the p-adic delta-distribution considered as a generalized function, yet coincide on point values with the latter.

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Eberhard Mayerhofer. 2005-08-01. On the characterization of p-adic Colombeau-Egorov generalized functions by their point values. https://arxiv.org/abs/math/0508027

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