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

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 9(Q(p)(n)) uniquely. We further show in a more general way that for an Egorov algebra 9(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 9(M, R) is given. Elements of 9(Q(p)(n)) are constructed which differ from the p-adic delta-distribution considered as an element of 9(Q(p)(n)), yet coincide on point values with the latter. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.