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  Volume 6, Issue 4, Article 94
 
On the Absolute Convergence of Small Gaps Fourier Series of Functions of $\varphi \bigwedge BV $
    Authors: R.G. Vyas,  
    Keywords: Fourier series with small gaps, Absolute convergence of Fourier series and $varphiwedge$-bounded variation.  
    Date Received: 06/07/05  
    Date Accepted: 29/07/05  
    Subject Codes:

42A16, 42A28, 26A45.

  
    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 qgeq1$. Here we obtain a sufficiency condition for the convergence of the series $ sum_{kin Z}mid widehat{f} (n_k)mid^beta$ (0

         
       
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