Open Access
Winter 2011 On the coefficients of Vilenkin-Fourier series with small gaps
Bhikha Lila Ghodadra
Kyoto J. Math. 51(4): 891-900 (Winter 2011). DOI: 10.1215/21562261-1424902


The Riemann-Lebesgue lemma shows that the Vilenkin-Fourier coefficient (n) is of o(1) as n for any integrable function f on Vilenkin groups. However, it is known that the Vilenkin-Fourier coefficients of integrable functions can tend to zero as slowly as we wish. The definitive result is due to B. L. Ghodadra for functions of certain classes of generalized bounded fluctuations. We prove that this is a matter only of local fluctuation for functions with the Vilenkin-Fourier series lacunary with small gaps. Our results, as in the case of trigonometric Fourier series, illustrate the interconnection between ‘localness’ of the hypothesis and type of lacunarity and allow us to interpolate the results.


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Bhikha Lila Ghodadra. "On the coefficients of Vilenkin-Fourier series with small gaps." Kyoto J. Math. 51 (4) 891 - 900, Winter 2011.


Published: Winter 2011
First available in Project Euclid: 10 November 2011

zbMATH: 1229.42031
MathSciNet: MR2854157
Digital Object Identifier: 10.1215/21562261-1424902

Primary: 42C10
Secondary: 26D15 , 43A40 , 43A75

Rights: Copyright © 2011 Kyoto University

Vol.51 • No. 4 • Winter 2011
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