On the fourier transforms of an interesting class of measures期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On the fourier transforms of an interesting class of measures

Authors:	J. R. Blum Bernard Epstein

Affiliation:	(1) The University of New Mexico, USA

Abstract:	Let {X _k,k=1,2,…} be a sequence of independent binomial variables, with $P{ X_k = 1} = 1 - P{ X_k = 0} = P_k cdot Let Y = sumlimits_{k = 1}^infty {X_k /2^k and hat mu (t)} be$ the Fourier transform of the distribution ofY. Finally denote lim [P _k − 1/2] byδ. We haveTheorem. $(4/pi )delta leqq overline {mathop {lim }limits_{x to infty } } left\| {hat mu (t)} right\| leqq 2delta$ Research supported by N.S.F. Grant GP-25736. Research supported by N.S.F. Grant GP-12365.

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