Algebras of non-Archimedean measures on groups
نویسنده
چکیده
Quasi-invariant measures with values in non-Archimedean fields on a group of diffeomorphisms were constructed for non-Archimedean manifolds M in [Lud96, Lud99t]. On non-Archimedean loop groups and semigroups they were provided in [Lud98s, Lud00a, Lud02b]. A Banach space over a local field also serves as the additive group and quasi-invariant measures on it were studied in [Lud03s2, Lud96c]. This article is devoted to the investigation of properties of quasi-invariant measures with values in non-Archimedean fields that are important for analysis on topological groups and for construction of irreducible representations. The following properties are investigated: (1) convolutions of measures and functions, (2) continuity of functions of measures, (3) non-associative algebras generated with the help of quasi-invariant measures. The theorems given below show that many differences appear to be between locally compact and non-locally compact groups. The groups considered below are supposed to have structure of Banach manifolds over the corresponding fields.
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