×

Nongeometric convergence of best \(L_ p\) (p\(\neq 2)\) polynomial approximants. (English) Zbl 0721.41036

Summary: For an arbitrary function f analytic in the disk D: \(| z| <1\) and continuous in \(\bar D,\) we show that geometric convergence in D of best \(L_ p\) (1\(\leq p\leq \infty)\) polynomial approximants to f on C: \(| z| =1\) is assumed only when \(p=2\).

MSC:

41A50 Best approximation, Chebyshev systems
41A10 Approximation by polynomials
PDFBibTeX XMLCite
Full Text: DOI