On the Convergence of the Linear Means of Jacobi Series at Lebesgue Points in the Case of Half-Integer $\alpha$

S. G. Kal'nei

Moscow State Institute of Electronic Technology (Technical University)

Abstract: 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, Lebesgue point, Cesàro summability, antipolar condition, Cesàro means, Abel transformation, Vallée-Poussin kernel.

UDC: 517.5

Received: 14.10.2004
Revised: 22.09.2005

DOI: 10.4213/mzm2800

 English version: Mathematical Notes, 2006, 80:2, 188–198

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