In [0,Π] we consider the complete orthogonal system Pn associated to the weight function ψ = r(2r - l)n-1 sin2 Ø(r2 - (2r - l)cos2 Øxs)-1 and we study mean and pointwise convergence of series expansions with respect to the system Pn in Lp([0, 7r], ch/>). This weight function, and the corresponding system Pn arise from the study of Gelfand transforms of radial functions on a finitely generated free group Fr and our results can be interpreted in terms of multipliers theory on Fr
Kuhn, M. (1984). Convergence of Fourier series expansion related to free groups. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 92(1), 31-36 [10.1090/S0002-9939-1984-0749884-9].
Convergence of Fourier series expansion related to free groups
KUHN, MARIA GABRIELLA
1984
Abstract
In [0,Π] we consider the complete orthogonal system Pn associated to the weight function ψ = r(2r - l)n-1 sin2 Ø(r2 - (2r - l)cos2 Øxs)-1 and we study mean and pointwise convergence of series expansions with respect to the system Pn in Lp([0, 7r], ch/>). This weight function, and the corresponding system Pn arise from the study of Gelfand transforms of radial functions on a finitely generated free group Fr and our results can be interpreted in terms of multipliers theory on Fr
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