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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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