✦ LIBER ✦
A Cohen type inequality for Fourier expansions of orthogonal polynomials with a non-discrete Gegenbauer-Sobolev inner product
✍ Scribed by Bujar Xh. Fejzullahu
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 156 KB
- Volume
- 284
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
Abstract
Let __d__μ(x) = (1 − x^2^)^α−1/2^dx,α> − 1/2, be the Gegenbauer measure on the interval [ − 1, 1] and introduce the non‐discrete Sobolev inner product
where λ>0. In this paper we will prove a Cohen type inequality for Fourier expansions in terms of the polynomials orthogonal with respect to the above inner product. Results on divergence for Cesàro means of Gegenbauer‐Sobolev expansions are deduced. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim