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Density of spaces of trigonometric polynomials with frequencies from a subgroup in \(L^\alpha\)-spaces. (Les espaces de polynômes trigonométriques avec fréquences dans un sous-groupe sont denses dans les espaces \(L^\alpha\).) (English. French summary) Zbl 1390.43001

Summary: Let \(G\) be an LCA group, \(H\) a closed subgroup, \(\Gamma\) the dual group of \(G\) and \(\mu\) be a regular finite non-negative Borel measure on \(\Gamma\). We give some necessary and sufficient conditions for the density of the set of trigonometric polynomials on \(\Gamma\) with frequencies from \(H\) in the space \(L^\alpha(\mu), \alpha \in(0, \infty)\).

MSC:

43A15 \(L^p\)-spaces and other function spaces on groups, semigroups, etc.
42A10 Trigonometric approximation
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