Abstract
AbstractWe 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 𝒢(ℚn p ) uniquely. We further show in a more general way that for an Egorov algebra 𝒢(M, R) of generalized functions on a locally compact ultrametric space (M, d) taking values in a nontrivial 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 𝒢(M, R) is given. Elements of 𝒢(ℚn p ) are constructed which differ from the p ‐adic δ ‐distribution considered as an element of 𝒢(ℚn p ), yet coincide on point values with the latter. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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