Convergence in L p -norm of Fourier series on the complete product of quaternion groups with bounded orders |
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Authors: | György Gát Rodolfo Toledo |
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Affiliation: | 1. College of Nyíregyháza, Inst. of Math. and Comp. Sci., Nyíregyháza, P. O. Box 166, H-4400, Hungary
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Abstract: | A well-known result for Vilenkin systems is the fact that for all 1 < p < ∞ the n-th partial sums of Fourier series of all functions in the space L p converge to the function in L p -norm. This statement can not be generalized to any representative product system on the complete product of finite non-abelian groups, but even then it is true for the complete product of quaternion groups with bounded orders and monomial representative product system ordered in a specific way. |
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Keywords: | Fourier analysis Walsh-Paley system representative product systems complete product of quaternion groups convergence in norm |
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