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AMS Subj. Classification: MSC2010: 42C10, 43A50, 43A75
We perform analysis of certain aspects of approximation in multiplicative systems
that appear as duals of ultrametric structures, e.g. in cases of local fields, totally disconnected
Abelian groups satisfying the second axiom of countability or more general ultrametric spaces
that do not necessarily possess a group structure. Using the fact that the unit sphere of a
local field is a Vilenkin group, we introduce a new concept of differentiation...
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