Mean and almost everywhere convergence of Fourier-Neumann series
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1
Universidad de La Rioja
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2
Universidad de Zaragoza
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ISSN: 0022-247X
Year of publication: 1999
Volume: 236
Issue: 1
Pages: 125-147
Type: Article
More publications in: Journal of Mathematical Analysis and Applications
Abstract
Let Jμ denote the Bessel function of order μ. The functions x-α/2-β/2-1/2Jα+β+2n+1(x 1/2), n=0,1,2,..., form an orthogonal system in L2((0,∞),xα+βdx) when α+β-1. In this paper we analyze the range of p, α, and β for which the Fourier series with respect to this system converges in the Lp((0,∞),xαdx)-norm. Also, we describe the space in which the span of the system is dense and we show some of its properties. Finally, we study the almost everywhere convergence of the Fourier series for functions in such spaces. © 1999 Academic Press.