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- W1967491464 abstract "The Riemann-Lebesgue lemma shows that the Vilenkin-Fourier coefficient f̂(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." @default.
- W1967491464 created "2016-06-24" @default.
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- W1967491464 date "2011-01-01" @default.
- W1967491464 modified "2023-09-24" @default.
- W1967491464 title "On the coefficients of Vilenkin-Fourier series with small gaps" @default.
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- W1967491464 doi "https://doi.org/10.1215/21562261-1424902" @default.
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