Georgian Mathematical Journal 13 (2006), No. 3, 581--584
Copyright Heldermann Verlag 2006
Fourier Series with Small Gaps
Rajendra G. Vyas
Dept. of Mathematics, Faculty of Science, Maharaja Sayajirao University of Baroda, Vadodara-390002, Gujarat, India
drrgvyas@yahoo.com
[Abstract-pdf]
Let $f$ be a $2\pi$-periodic function in $L^1[-\pi,\pi]$ and $\sum\limits_{k=-\infty}^\infty \widehat{f}(n_k) e^{in_kx}$ be its lacunary Fourier series with small gaps. We have estimated Fourier coefficients of $f$ if it is of $\varphi \bigwedge BV$ locally. We have also obtained a precise interconnection between the lacunarity in such series and the localness of the hypothesis to be satisfied by the generic function which allows us to the interpolate the results concerning lacunary series and non-lacunary series.
Keywords: Fourier series with small gaps, Order of magnitude of Fourier coefficients, Phi-bigwedge-bounded variations.
MSC: 42A16, 42A55
[ Fulltext-pdf (178 KB)] for subscribers only.