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Microlocal analysis

Microlocal analysis is a branch of mathematical analysis that studies functions, generalized functions and partial differential equations by localizing them both in position and in frequency. The main idea is to describe a singularity not only by the point at which it occurs, but also by the cotangent direction in which it occurs. The term microlocal…

Art, Overview & Propagation of singularities

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Overview

Mathematical analysisGeneralized functionsPartial differential equationsCotangent directionPhase space
17 related topics

Propagation of singularities

Riemannian manifoldGeodesic flowLorentzian geometryNull geodesics
4 related topics

Wave front set

Dirac delta distributionConormal bundle
2 related topics

Pseudodifferential operators

Symbol
1 related topics

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Overview

Wave front set

Pseudodifferential operators

  • Symbol Symbol of a differential operator

Propagation of singularities

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Microlocal analysis

Nodes29
Edges28
Triples16
Avg. degree1.93
Density0.068966
Components1

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Microlocal analysis

Top relations

related to Propagation of singularities · 10
Microlocal analysis → For, Hamiltonian, In, In Lorentzian, Let, Pu, Riemannian, The, The Hamiltonian, This
related to Microlocal smoothness · 5
Microlocal analysis → Fourier, If, Microlocal, On, Thus
is a · 1
Microlocal analysis → branch of mathematical analysis that studies functions

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Important terminology

displaystyle microlocal analysis operators wave singularities xi set symbol distribution front point fourier operator differential cotangent smooth principal elliptic partial

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Microlocal analysisis abranch of mathematical analysis that studies functions0.90text
Microlocal analysisrelated to Microlocal smoothnessOn0.60section
Microlocal analysisrelated to Microlocal smoothnessFourier0.60section
Microlocal analysisrelated to Microlocal smoothnessIf0.60section
Microlocal analysisrelated to Microlocal smoothnessMicrolocal0.60section
Microlocal analysisrelated to Microlocal smoothnessThus0.60section
Microlocal analysisrelated to Propagation of singularitiesFor0.60section
Microlocal analysisrelated to Propagation of singularitiesLet0.60section
Microlocal analysisrelated to Propagation of singularitiesThe Hamiltonian0.60section
Microlocal analysisrelated to Propagation of singularitiesThe0.60section
Microlocal analysisrelated to Propagation of singularitiesPu0.60section
Microlocal analysisrelated to Propagation of singularitiesThis0.60section

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