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	Título: On The Convergence Of Eckf (Nkx)
	Autor: Berkes Istvan/ Weber Michel	Precio: $726.22
	Editorial: American Mathematical Society	Año: 2009
	Tema: Matematicas, Algebra, Textos	Edición: 1ª
	Sinopsis	ISBN: 9780821843246
	Let f be a periodic measurable function and x (nk) an increasing sequence of positive integers. The authors study conditions under which the series k=1 Ckf(nkx)_ converges in mean and for almost every x. There is a wide classical literature on this problem going back to the 30's, but the results for general f are much less complete than in the trigonometric case f(x) = sin x. As it turns out, the convergence properties of k=1 ckf(nkx) in the general case are determined by a delicate interplay between the coefficient sequence (ck), the analytic properties of f and the growth speed and number-theoretic properties of (nk). In this paper the authors give a general study of this convergence problem, prove several new results and improve a number of old results in the field. They also study the case when the nk are random and investigate the discrepancy the sequence {nkx} mod 1. Table of Contents Introduction Mean convergence Almost everywhere convergence: Sufficient conditions Almost everywhere convergence: Necessary conditions Random sequences Discrepancy of random sequences E\{S_n x\}E Some open problems Bibliography

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