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Bases Consisting of Rational Functions of Uniformly Bounded Degrees or More General Functions

✍ Scribed by Pencho Petrushev

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 347 KB
Volume: 174
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2000.3588

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✦ Synopsis

We prove in this paper the existence of a Schauder basis for C[0, 1] consisting of rational functions of uniformly bounded degrees. This solves an open question of some years standing concerning the possible existence of such bases. This result follows from a more general construction of bases on R and [0, 1]. We prove that the new bases are unconditional bases for L p , 1<p< , and Besov spaces. On [0, 1], they are Schauder bases for C[0, 1] as well. The new bases are utilized for nonlinear approximation.

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