Geodesic
WEAK BEHAVIOUR OF FOURIER-NEUMANN SERIES
Glasgow mathematical journal, Tome 45 (2003) no. 1, pp. 97-104

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DOI

Let $J_\mu$ denote the Bessel function of order $\mu$. The functions $x^{-\alpha-1} J_{\alpha+2n+1}(x), n=0,1,2,\ldots,$ form an orthogonal system in the space $L^2((0,\infty), x^{2\alpha+1}dx)$ when $\alpha >{-}1$. In this paper we prove that the Fourier series associated to this system is of restricted weak type for the endpoints of the interval of mean convergence, while it is not of weak type if $\alpha\,{\ge}\,0$.
DOI : 10.1017/S0017089502001039
Mots-clés : 42C10, 44A05 
CIAURRI, ÓSCAR; PÉREZ, MARIO; VARONA, JUAN L. WEAK BEHAVIOUR OF FOURIER-NEUMANN SERIES. Glasgow mathematical journal, Tome 45 (2003) no. 1, pp. 97-104. doi: 10.1017/S0017089502001039
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     title = {WEAK {BEHAVIOUR} {OF} {FOURIER-NEUMANN} {SERIES}},
     journal = {Glasgow mathematical journal},
     pages = {97--104},
     year = {2003},
     volume = {45},
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     doi = {10.1017/S0017089502001039},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089502001039/}
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