Schauder basis information

In mathematics, a Schauder basis or countable basis is similar to the usual (Hamel) basis of a vector space; the difference is that Hamel bases use linear...

forms a basis for L2[0,1]. Basis (linear algebra) (Hamel basis) Schauder basis (in a Banach space) Dual basis Biorthogonal system (Markushevich basis) Orthonormal...

cost of an asset Basis function Basis (linear algebra) Dual basis Orthonormal basis Schauder basis Basis (universal algebra) Basis of a matroid Generating...

is also an unconditional Schauder basis for the space Lp([0, 1]) when 1 < p < ∞. The Franklin system provides a Schauder basis in the disk algebra A(D)...

topological methods in nonlinear analysis. Banach–Schauder theorem Schauder basis Schauder estimates Schauder fixed point theorem List of Polish mathematicians...

Orthogonal basis Basis (linear algebra) – Set of vectors used to define coordinates Orthonormal frame – Euclidean space without distance and angles Schauder basis –...

without a Schauder basis. Robert C. James characterized reflexivity in Banach spaces with a basis: the space X {\displaystyle X} with a Schauder basis is reflexive...

(mathematics) Orthonormal frame – Euclidean space without distance and angles Schauder basis – Computational tool Total set – subset of a topological vector space...

system, and like the trigonometric system, this basis is not unconditional, nor is the system a Schauder basis in L 1 [ 0 , 1 ] {\displaystyle L^{1}[0,1]}...

Banach spaces. Schauder bases were described by Juliusz Schauder in 1927. Let V denote a Banach space over the field F. A Schauder basis is a sequence...

existence of a vector space basis for such spaces may require Zorn's lemma. However, a somewhat different concept, the Schauder basis, is usually more relevant...

also a Markushevich basis; the converse is not true in general. An example of a Markushevich basis that is not a Schauder basis is the sequence { e 2...

The spaces c0 and ℓp (for 1 ≤ p < ∞) have a canonical unconditional Schauder basis {ei | i = 1, 2,...}, where ei is the sequence which is zero but for...

space has an infinite-dimensional subspace that admits an unconditional Schauder basis. After this, Gowers turned to combinatorics and combinatorial number...

theory Fourier series Function approximation Orthonormal basis Padé approximant Schauder basis Kalman filter N. I. Achiezer (Akhiezer), Theory of approximation...

B_{V}}\sum _{w\in B_{W}}B(v,w)(v\otimes w)} making these maps similar to a Schauder basis for the vector space Hom ( V , W ; F ) {\displaystyle {\text{Hom}}(V...

separable Frechet space that contains a Schauder basis possesses the approximation property. Every space with a Schauder basis has the AP (we can use the projections...

admits a countably infinite Schauder basis rather than an orthonormal basis in the sense of linear algebra (Hamel basis). As, technically, they are not...

function f be expressed in terms of the eigenfunctions (are they a Schauder basis) and under what circumstances does a point spectrum or a continuous...

space James' space, a Banach space that has a Schauder basis, but has no unconditional Schauder Basis. Also, James' space is isometrically isomorphic...

polynomially reflexive Banach space. Distortion problem Sequence space, Schauder basis James' space see for example Casazza & Shura (1989), p. 8; Lindenstrauss...

in prison by the Gestapo, Warsaw Juliusz Schauder 1899–1943 Polish Schauder fixed point theorem, Schauder basis Jewish executed by the Gestapo, Lviv Włodzimierz...

t}{T}}\right)} is a Schauder basis of H p e r 1 ( ( 0 , T ) , C n ) {\displaystyle H_{\rm {per}}^{1}((0,T),\mathbb {C} ^{n})} and forms a :Hilbert basis of the Hilbert...

space has an infinite-dimensional subspace that admits an unconditional Schauder basis. Pietsch, Albrecht (2007). History of Banach spaces and linear operators...