Sequences, series, summability Concept
Uniform convergence
Summary
A sequence of functions converges uniformly when the largest distance between and the limit tends to zero. Uniform limits keep continuity, and they commute with integration. The node uniform convergence gives the precise definition.
Where this leads
27 pages build on this one.
- Hilbert–Schmidt expansion theorem
- L2 convergence of Fourier series
- Dini–Lipschitz criterion
- Abel's lemma for multiple power series
- Egorov's theorem
- Oka–Weil theorem
- Uniform convergence of absolutely summable Fourier series
- Uniform algebra
- Domain of convergence of a power series
- Littlewood's three principles
- Glivenko–Cantelli theorem
- Lidskii's trace formula for integral operators
- Density of trigonometric polynomials in continuous functions
- Oka manifold
- Runge domain
- Fourier basis of L2 of the circle
- Resolvent kernel
- Mercer's theorem
- Topology of uniform convergence
- Convergence of Fourier series
- Basel problem via Fourier series
- Decay of Fourier coefficients and smoothness
- Montessus de Ballore's theorem
- Baker–Gammel–Wills conjecture
- Expansion in spherical harmonics
- Runge's phenomenon
- Faber's theorem on interpolation
Further reading
- Web https://en.wikipedia.org/wiki/Uniform_convergence, lead section
About this page
| Tag | 08VZ57PT26 |
|---|---|
| URI | m2://08VZ57PT26 |
| Kind | concept |
| Writing | W1 stated |
| MSC | 40A30 |
| Specializes | Pointwise convergence |
| Same as |
Markdown · JSON · Edit on GitHub
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)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Definitions
Special cases
Used by
- Hilbert–Schmidt expansion theorem
- Dini–Lipschitz criterion
- Abel's lemma for multiple power series
- Egorov's theorem
- Oka–Weil theorem
- Uniform convergence of absolutely summable Fourier series
- Uniform algebra
- Littlewood's three principles
- Glivenko–Cantelli theorem
- Density of trigonometric polynomials in continuous functions
- Runge domain
- Resolvent kernel
- Mercer's theorem
- Topology of uniform convergence
- Convergence of Fourier series
- Montessus de Ballore's theorem
- Baker–Gammel–Wills conjecture
- Expansion in spherical harmonics
- Runge's phenomenon
- Faber's theorem on interpolation