Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Hilbert_space
|
| gptkbp:category |
gptkb:basis_(mathematics)
|
| gptkbp:defines |
A sequence (x_n) in a Banach space X such that every element x in X can be written uniquely as a convergent series x = sum a_n x_n.
|
| gptkbp:distinctFrom |
Hamel basis uses finite linear combinations, Schauder basis uses infinite series
|
| gptkbp:example |
The sequence of unit vectors in l^p spaces (1 ≤ p < ∞) forms a Schauder basis
|
| gptkbp:field |
functional analysis
|
| gptkbp:generalizes |
orthonormal basis in Hilbert spaces
|
| https://www.w3.org/2000/01/rdf-schema#label |
Schauder basis
|
| gptkbp:introducedIn |
1927
|
| gptkbp:namedAfter |
gptkb:Juliusz_Schauder
|
| gptkbp:notion |
Topological, depends on convergence in norm
|
| gptkbp:property |
Allows unique representation of elements as convergent series
|
| gptkbp:relatedTo |
gptkb:Hamel_basis
|
| gptkbp:usedIn |
infinite-dimensional vector spaces
|
| gptkbp:bfsParent |
gptkb:Juliusz_Schauder
gptkb:Eileen_Schauder |
| gptkbp:bfsLayer |
6
|