Geodesic
On the Convergence of the Linear Means of Jacobi Series at Lebesgue Points in the Case of Half-Integer~$\alpha$
Matematičeskie zametki, Tome 80 (2006) no. 2, pp. 193-203

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We investigate the convergence of the linear means of the Fourier–Jacobi series of functions $f(x)$ from the weight space $L_{\alpha,\beta}[-1,1]$ for $x=1$ for the case in which this point is a Lebesgue point for $f$. We establish sufficient summability conditions depending on the behavior of the function on the closed interval $[-1,0]$ and on the properties of the matrix involved in the summation method.
Keywords: Jacobi series, linear means of Jacobi series, Cesàro summability, Cesàro means
Mots-clés : Lebesgue point, antipolar condition, Abel transformation, Vallée-Poussin kernel. 
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     author = {S. G. Kal'nei},
     title = {On the {Convergence} of the {Linear} {Means} of {Jacobi} {Series} at {Lebesgue} {Points} in the {Case} of {Half-Integer~}$\alpha$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {193--203},
     publisher = {mathdoc},
     volume = {80},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_80_2_a4/}
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S. G. Kal'nei. On the Convergence of the Linear Means of Jacobi Series at Lebesgue Points in the Case of Half-Integer~$\alpha$. Matematičeskie zametki, Tome 80 (2006) no. 2, pp. 193-203. http://geodesic.mathdoc.fr/item/MZM_2006_80_2_a4/