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  • 1 Moscow Institute of Electronic Technology (Technical University) Russia, Moscow, g. Zelenograd, 124498, proezd 4806, dom 5 Russia, Moscow, g. Zelenograd, 124498, proezd 4806, dom 5
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Summary  

The problem of convergence of linear means is considered for the Laguerre-Fourier  series of continuous functions. An upper estimate is obtained for the Laguerre-Lebesgue function  in terms  of the entries of the matrix which determines the linear summability method  in question.  This allows us to prove for such series an analogue of the well-known theorem by S. M. Nikol'skii which provides necessary and sufficient conditions for the summability  of trigonometric Fourier series. A theorem on the regularity of the summability methods  is also  established.