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Obermaier, J.

A continuous function space with a Faber basis.

J. Approx. Theory 125, 303-312 (2003)
DOI
Open Access Green as soon as Postprint is submitted to ZB.
Let S subset of R be compact with #S = infinity and let C(S) be the set of all real continuous functions on S. We ask for an algebraic polynomial sequence (P-n)(n=0)(infinity) with deg P-n = n such that every f is an element of C(S) has a unique representation f = Sigma(i=0)(infinity) alpha(i)P(i) and call such a basis Faber basis. In the special case of S = S-q = {q(k); k is an element of N-0} boolean OR {0}, 0 < q < 1, we prove the existence of such a basis. A special orthonormal Faber basis is given by the so-called little q-Legendre polynomials. Moreover, these polynomials state an example with A (S-q) not equal U(S-q) = C(S-q), where A(S-q) is the so-called Wiener algebra and U(S-q) is the set of all f is an element of C(S-q) which are uniquely represented by its Fourier series.
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Publication type Article: Journal article
Document type Scientific Article
Keywords continuous function; polynomial; basis; little q-Legendre polynomials; Fourier series; Wiener algebra; Q-LEGENDRE POLYNOMIALS
ISSN (print) / ISBN 0021-9045
e-ISSN 1096-0430
Journal Journal of Approximation Theory
Quellenangaben Volume: 125, Issue: 2, Pages: 303-312 Article Number: , Supplement: ,
Publisher Elsevier
Reviewing status Peer reviewed
Institute(s) Institute of Biomathematics and Biometry (IBB)