Smooth function
Summary
A smooth function is a function with continuous derivatives of all orders. Smoothness is the top of the scale of differentiability classes . The node smooth function gives the precise definition.
Where this leads
89 pages build on this one.
- Stationary phase approximation
- Hopf bifurcation
- Transcritical bifurcation
- Malgrange preparation theorem
- Horocycle flow
- Catastrophe theory
- Morse–Bott function
- Elliptic regularity
- Mollifier
- Navier–Stokes existence and smoothness
- q-convex manifold
- Maass wave form
- Smoothing by convolution
- Differential of a smooth map
- Levi form
- Geodesic flow on a locally symmetric space
- Deformation quantization
- Automorphic form
- Spectral decomposition theorem
- Lie bracket of vector fields
- Fredholm property of elliptic operators
- Oscillatory integral
- Thom–Mather isotopy lemmas
- Gradient flow on a manifold
- Computed tomography as an inverse problem
- Frölicher space
- Graded manifold
- Morse index
- Smoothness and analyticity of harmonic functions
- Quantum ergodicity
- Local solvability
- Tangent bundle
- Diffeology
- C-infinity ring
- Anosov flow
- Manifold with corners
- Quantum unique ergodicity conjecture
- Harish-Chandra character
- Nondegenerate critical point
- Germ of a smooth function
- Lie group action
- Schwartz space
- Fefferman's expansion of the Bergman kernel
- Submersion
- Bogdanov–Takens bifurcation
- Radon inversion formula
- Absolutely monotonic function
- Smooth dynamical system
- Relaxation oscillation
- Lie group
- Lie groupoid
- Regular value theorem
- Morse function
- Hyperbolic set
- Versal unfolding
- (p,q)-form
- Wave front set
- Parametric transversality theorem
- Van der Corput lemma
- Domain of finite type
- Axiom A
- Completely monotone function
- Hypoelliptic operator
- Decay of the Fourier transform of surface measure
- Mather's stability theorem
- Saddle-node bifurcation
- Integral transforms of tempered distributions
- Pitchfork bifurcation
- Jet
- Geodesic flow
- Smooth structure
- Bifurcation set
- Thom–Mather stratified space
- Range conditions for the Radon transform
- Smooth manifold
- Anosov diffeomorphism
- Section of a vector bundle
- Stability conjecture
- Decay of Fourier coefficients and smoothness
- Hadamard's lemma
- Approximation by convolution with mollifiers
- Sard–Smale theorem
- Morrey's inequality
- Sard's theorem
- Symbol class
- Immersion
- Manifold of smooth mappings
- Colombeau algebra
- Stein–Tomas restriction theorem
Further reading
- Web https://en.wikipedia.org/wiki/Smoothness, lead section
About this page
| Tag | 0V33BNKZ9S |
|---|---|
| URI | m2://0V33BNKZ9S |
| Kind | concept |
| Writing | W1 stated |
| MSC | 26E10 |
| Specializes | Continuous function |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
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What links here
Special cases
Definitions
Used by
- Stationary phase approximation
- Hopf bifurcation
- Transcritical bifurcation
- Malgrange preparation theorem
- Catastrophe theory
- Morse–Bott function
- Elliptic regularity
- Mollifier
- Navier–Stokes existence and smoothness
- q-convex manifold
- Maass wave form
- Smoothing by convolution
- Differential of a smooth map
- Levi form
- Deformation quantization
- Automorphic form
- Lie bracket of vector fields
- Oscillatory integral
- Gradient flow on a manifold
- Frölicher space
- Graded manifold
- Morse index
- Smoothness and analyticity of harmonic functions
- Local solvability
- Tangent bundle
- Diffeology
- C-infinity ring
- Manifold with corners
- Harish-Chandra character
- Nondegenerate critical point
- Germ of a smooth function
- Lie group action
- Schwartz space
- Fefferman's expansion of the Bergman kernel
- Submersion
- Bogdanov–Takens bifurcation
- Absolutely monotonic function
- Relaxation oscillation
- Lie group
- Lie groupoid
- Morse function
- Versal unfolding
- (p,q)-form
- Wave front set
- Van der Corput lemma
- Domain of finite type
- Completely monotone function
- Hypoelliptic operator
- Decay of the Fourier transform of surface measure
- Saddle-node bifurcation
- Pitchfork bifurcation
- Jet
- Smooth structure
- Bifurcation set
- Smooth manifold
- Section of a vector bundle
- Decay of Fourier coefficients and smoothness
- Hadamard's lemma
- Approximation by convolution with mollifiers
- Sard's theorem
- Symbol class
- Immersion
- Colombeau algebra