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  Volume 6, Issue 1, Article 23
 
On the Absolute Convergence of Small Gaps Fourier Series of Functions of $\bigwedge BV^{(p)}$
    Authors: R.G. Vyas,  
    Keywords: Fourier series with small gaps, Absolute convergence of Fourier series, p-$bigwedge $-bounded variation.  
    Date Received: 18/10/04  
    Date Accepted: 29/11/04  
    Subject Codes:

42Axx

  
    Editors: Laszlo Leindler,  
 
    Abstract:

Let $ f$ be a $ 2pi$ periodic function in $ L^1[0,2pi]$ and $ sum_{k=-infty}^infty widehat{f}(n_k) e^{in_kx}$ be its Fourier series with `small' gaps $ n_{k+1}-n_kgeq qgeq 1$. Here we have obtained sufficiency conditions for the absolute convergence of such series if $ f$ is of $ bigwedge BV^{(p)}$ locally. We have also obtained a beautiful interconnection between lacunary and non-lacunary Fourier series.

         
       
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