p-Adic Colombeau-Egorov type theory of generalized functions

The p‐adic Colombeau‐Egorov algebra of generalized functions on ℚnp 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 ℝn are not determined by their pointvalues on ℝn, p‐adic Colombeau‐Egorov generalized functions are uniquely determined by their pointvalues on ℚnp. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)