p-adic Colombeau-Egorov type theory of generalized functions

The p-adic Colombeau-Egorov algebra of generalized functions on Q(p)(n) is constructed. For generalized functions the operations of multiplication, Fourier-transform, convolution, taking pointvalues are defined. The operations of (fractional) partial differentiation and (fractional) partial integration are introduced by the Vladimirov's pseudodifferential operator. The products of Bruhat-Schwartz distributions are well defined as elements of this algebra. In contrast to the "usual" Colombeau and Egorov C-theories, where generalized functions on R-n are not determined by their pointvalues on R-n, p-adic Colombeau-Egorov generalized functions are uniquely determined by their pointvalues on Q(p)(n). (C) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.