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Smoothness

In mathematical analysis, the smoothness describes the number of times a function can be differentiated without producing discontinuities. The smoothness, or differentiability class, is an integer k {\displaystyle k} such that a function has all derivatives up to order k {\displaystyle k} , and such that all of these derivatives are continuous. One says…

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Differentiability classes

Function spaces

Basic properties

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Smoothness

Nodes88
Edges87
Triples31
Avg. degree1.98
Density0.022727
Components1

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Smoothness

Top relations

related to Smoothness and the Fourier transform · 11
Smoothness → Conversely, For, Fourier, Fourier-transform, Laplace, Paley, Sobolev, These, This, Under, Wiener
see also · 10
Smoothness → Concept, Discontinuity, Fitting, Integer, Mathematical, Notion, Point, Ratio, Smoothing, TheoremNon-analytic
related to Smooth functions on and between manifolds · 6
Smoothness → Given, Leibniz, On, Similarly, That, Xf

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Important terminology

displaystyle function functions smooth class continuous differentiable open analytic derivatives differentiability infty defined also set spaces subsets integer manifolds said

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
the inverse function theoreminstance ofis a hypothesis in local results0.80text
the implicit function theoreminstance ofis a hypothesis in local results0.80text
bump functionsinstance ofexamples0.80text
the Paleyinstance ofThese relationships are related to results0.80text
Smoothnessrelated to Smooth functions on and between manifoldsGiven0.60section
Smoothnessrelated to Smooth functions on and between manifoldsSimilarly0.60section
Smoothnessrelated to Smooth functions on and between manifoldsOn0.60section
Smoothnessrelated to Smooth functions on and between manifoldsThat0.60section
Smoothnessrelated to Smooth functions on and between manifoldsXf0.60section
Smoothnessrelated to Smooth functions on and between manifoldsLeibniz0.60section
Smoothnessrelated to Smoothness and the Fourier transformUnder0.60section
Smoothnessrelated to Smoothness and the Fourier transformLaplace0.60section

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