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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].

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
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Full Text: MNR