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Wave front set

In mathematical analysis, more precisely in microlocal analysis, the wave front (set) WF(f) characterizes the singularities of a generalized function f, not only in space, but also with respect to its Fourier transform at each point. The term "wave front" was coined by Lars Hörmander around 1970.

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Wave front set

Nodes31
Edges30
Triples14
Avg. degree1.94
Density0.064516
Components1

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Wave front set

Top relations

related to Definition · 6
Wave front set → Fourier, Gamma, In Euclidean, More, Sigma, The
related to Example · 3
Wave front set → If, Schwartz, Then
related to Generalizations · 3
Wave front set → Localized, More, The
is a · 1
Wave front set → closed conical subset of the cotangent bundle T
has application · 1
Wave front set → The

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Important terminology

function set wave front smooth displaystyle fourier transform singular complement space direction singularities support also conical defined functions wf directions

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Wave front setis aclosed conical subset of the cotangent bundle T0.90text
Wave front sethas applicationThe0.60section
Wave front setrelated to DefinitionIn Euclidean0.60section
Wave front setrelated to DefinitionSigma0.60section
Wave front setrelated to DefinitionThe0.60section
Wave front setrelated to DefinitionFourier0.60section
Wave front setrelated to DefinitionMore0.60section
Wave front setrelated to DefinitionGamma0.60section
Wave front setrelated to ExampleIf0.60section
Wave front setrelated to ExampleSchwartz0.60section
Wave front setrelated to ExampleThen0.60section
Wave front setrelated to GeneralizationsThe0.60section

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