Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 51, Number 4 (2011), 891-900.
On the coefficients of Vilenkin-Fourier series with small gaps
The Riemann-Lebesgue lemma shows that the Vilenkin-Fourier coefficient is of as for any integrable function 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.
Kyoto J. Math., Volume 51, Number 4 (2011), 891-900.
First available in Project Euclid: 10 November 2011
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
Secondary: 26D15: Inequalities for sums, series and integrals 43A40: Character groups and dual objects 43A75: Analysis on specific compact groups
Ghodadra, Bhikha Lila. On the coefficients of Vilenkin-Fourier series with small gaps. Kyoto J. Math. 51 (2011), no. 4, 891--900. doi:10.1215/21562261-1424902. https://projecteuclid.org/euclid.kjm/1320936737