Mean and almost everywhere convergence of Fourier-Neumann series

  1. Ciaurri, O. 1
  2. Guadalupe, J.J. 1
  3. Pérez, M. 2
  4. Varona, J.L. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidad de Zaragoza
    info

    Universidad de Zaragoza

    Zaragoza, España

    ROR https://ror.org/012a91z28

Revue:
Journal of Mathematical Analysis and Applications

ISSN: 0022-247X

Année de publication: 1999

Volumen: 236

Número: 1

Pages: 125-147

Type: Article

DOI: 10.1006/JMAA.1999.6442 SCOPUS: 2-s2.0-0000995361 WoS: WOS:000081963000008 GOOGLE SCHOLAR lock_openAccès ouvert editor

D'autres publications dans: Journal of Mathematical Analysis and Applications

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Résumé

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.