Rate of convergence of the conjugate Fourier integral and its Nörlund means


Abstract


In this paper, we give the rate of convergence of the conjugate Fourier integral of functions of bounded variation over (-\infty,\infty). Further, we give the rate of convergence of Nörlund means of the conjugate Fourier integral of f, where f is of bounded variation over every finite interval [a,b], -\infty < a< b <\infty. Also, in particular as corollary, we get the rate of convergence of (C,1) means of the conjugate Fourier integral.

Keywords: Nörlund summability; Cesàro summability; functions of bounded variation on $\mathbb{R}$; Conjugate Fourier integral

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