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Convergence of Fourier series expansion related to free groups


Author: G. Kuhn
Journal: Proc. Amer. Math. Soc. 92 (1984), 31-36
MSC: Primary 43A50; Secondary 20E05, 33A45, 42C10
DOI: https://doi.org/10.1090/S0002-9939-1984-0749884-9
MathSciNet review: 749884
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Abstract: In $ [0,\pi ]$ we consider the complete orthogonal system $ {P_n}$ associated to the weight function $ \psi = r(2r - 1){\pi ^{ - 1}}{\rm {si}}{{\rm {n}}^2}\theta {({r^2} - (2r - 1){\rm {co}}{{\rm {s}}^2}\theta )^{ - 1}}$ and we study mean and pointwise convergence of series expansions with respect to the system $ {P_n}$ in $ {L^p}([0,\pi ],d\psi )$. This weight function, and the corresponding system $ {P_n}$ arise from the study of Gelfand transforms of radial functions on a finitely generated free group $ {F_r}$ and our results can be interpreted in terms of multipliers theory on $ {F_r}$.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0749884-9
Article copyright: © Copyright 1984 American Mathematical Society

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