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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