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Harmonious set

In mathematics, a harmonious set is a subset of a locally compact abelian group on which every weak character may be uniformly approximated by strong characters. Equivalently, a suitably defined dual set is relatively dense in the Pontryagin dual of the group. This notion was introduced by Yves Meyer in 1970 and later turned out to play an important role…

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Map overview Semantic statistics

Harmonious set

Nodes22
Edges21
Triples10
Avg. degree1.91
Density0.090909
Components1

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Harmonious set

Top relations

related to Examples · 7
Harmonious set → Conversely, In, Interesting, Let, Pisot, Salem, Then
related to Properties · 2
Harmonious set → If, The
is a · 1
Harmonious set → subset of a locally compact abelian group on which every weak character may be uniformly approximated by strong characters

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Important terminology

harmonious set group compact every numbers weak character strong sets meyer algebraic finite real pisot number subset locally abelian may

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Harmonious setis asubset of a locally compact abelian group on which every weak character may be uniformly approximated by strong characters0.90text
Harmonious setrelated to ExamplesInteresting0.60section
Harmonious setrelated to ExamplesLet0.60section
Harmonious setrelated to ExamplesThen0.60section
Harmonious setrelated to ExamplesPisot0.60section
Harmonious setrelated to ExamplesIn0.60section
Harmonious setrelated to ExamplesSalem0.60section
Harmonious setrelated to ExamplesConversely0.60section
Harmonious setrelated to PropertiesIf0.60section
Harmonious setrelated to PropertiesThe0.60section

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