Article ID Journal Published Year Pages File Type
8900354 Journal of Mathematical Analysis and Applications 2018 14 Pages PDF
Abstract
Let G be a topological group. We investigate relations between two classes of “polynomial like” continuous functions on G defined, respectively, by the conditions 1) Δhn+1f=0 for every h∈G, and 2) Δhn+1Δhn⋯Δh1f=0 for every h1,⋯,hn+1∈G. It is shown that for many (but not all) groups these classes coincide. We consider also Montel type versions of the above conditions - when 1) and 2) hold only for h in a generating subset of G. Our approach is based on the study of the counterparts of the discussed classes for general representations of groups (instead of the regular representation).
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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