Weierstrass approximation theorem
GPTKB entity
Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Weierstrass_theorem
|
| gptkbp:appliesTo |
continuous functions
closed intervals |
| gptkbp:category |
approximation theory
|
| gptkbp:field |
mathematical analysis
|
| gptkbp:generalizes |
gptkb:Stone–Weierstrass_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Weierstrass approximation theorem
|
| gptkbp:implies |
polynomials are dense in the space of continuous functions on [a, b] with the uniform norm
|
| gptkbp:importantFor |
fundamental result in analysis
|
| gptkbp:namedAfter |
gptkb:Karl_Weierstrass
|
| gptkbp:provenBy |
constructive proof using Bernstein polynomials
|
| gptkbp:publishedIn |
gptkb:Journal_für_die_reine_und_angewandte_Mathematik
|
| gptkbp:relatedTo |
gptkb:Stone–Weierstrass_theorem
|
| gptkbp:state |
Every continuous real-valued function defined on a closed interval [a, b] can be uniformly approximated as closely as desired by a polynomial function.
|
| gptkbp:yearProved |
1885
|
| gptkbp:bfsParent |
gptkb:Karl_Weierstrass
|
| gptkbp:bfsLayer |
5
|