Albeverio, S.; Khrennikov, A. Yu.; Shelkovich, V. M. Associative algebras of \(p\)-adic distributions. (English. Russian original) Zbl 1098.46032 Proc. Steklov Inst. Math. 245, 22-33 (2004); translation from Tr. Mat. Inst. Steklova 245, 29-40 (2004). Summary: A \(p\)-adic Colombeau-Egorov algebra of generalized functions is constructed. A set of associated homogeneous \(p\)-adic distributions is introduced, and an associative algebra of asymptotic distributions generated by the linear span of the set of \(p\)-adic associated homogeneous distributions is constructed.For the entire collection see [Zbl 1087.46002]. Cited in 2 Documents MSC: 46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) 11S99 Algebraic number theory: local and \(p\)-adic fields 46F05 Topological linear spaces of test functions, distributions and ultradistributions 46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis PDF BibTeX XML Cite \textit{S. Albeverio} et al., in: Selected topics of \(p\)-adic mathematical physics and analysis. Collected papers. Dedicated to the 80th birthday of Academician Vasilii Sergeevich Vladimirov. Papers of the 1st conference on \(p\)-adic mathematical physics, Moscow, Russia, October 1--4, 2003. Transl. from the Russian. Moscow: Maik Nauka/Interperiodica. 22--33 (2004; Zbl 1098.46032); translation from Tr. Mat. Inst. Steklova 245, 29--40 (2004) Full Text: MNR