A lower estimate for the Lebesgue constants of linear means of Laguerre expansions

Authors: George Gasper and Walter Trebels

Dedicated to P. L. Butzer on the occasion of his 70th birthday in gratitude

Abstract:

S. G. Kal'nei derived a quite sharp necessary condition for the multiplier norm of a finite sequence in the setting of Fourier-Jacobi series on $L^1$ with "natural weight" (which ensures a nice convolution structure). In this paper, Kalnei's problem is considered in the setting of Laguerre series on weighted $L^1$-spaces; the admitted scale of weights contains in particular the appropriate "natural weights" occurring in transplantation and convolution.

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