On the mean summability of series by nonlinear basis

2017/04/06 by Hatice Aslan, Aslan, Hatice, Ali Guven +1
Mathematics · #41A10 #41A25 #41E30 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:41A10 #msc:41A25 #msc:41E30

paper · pdf · doi:10.48550/arxiv.1704.01825

19 pages

arxiv created 2017/04/06 · arxiv updated 2017/04/07

Abstract

The nonlinear signal processing has achieved a rapid process in the recent years. A family of nonlinear Fourier bases, as a typical family of mono-component signals, has been constructed and applied to signal processing. In this paper, the approximation properties of the partial sums and Ces?aro summability of series by the nonlinear Fourier basis are investigated in the Lp(T). Furthermore, these results are applied to the prove of Bernstein's inequalities for nonlinear trigonometric polynomials.

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