On the fourier transforms of an interesting class of measures

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1971 English Publisher:Springer Science and Business Media LLCJournal:Israel Journal of Mathematics, volume 10, pages 302-305 (issn: 0021-2172, eissn: 1565-8511,

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Authors: Blum, J. R.; Epstein, Bernard;

doi: 10.1007/bf02771647

On the fourier transforms of an interesting class of measures

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Abstract

Let {Xk,k=1,2,…} be a sequence of independent binomial variables, with\(P\{ X_k = 1\} = 1 - P\{ X_k = 0\} = P_k \cdot Let Y = \sum\limits_{k = 1}^\infty {X_k /2^k and \hat \mu (t)} be\) the Fourier transform of the distribution ofY. Finally denote lim [Pk − 1/2] byδ. We haveTheorem. \((4/\pi )\delta \leqq \overline {\mathop {\lim }\limits_{x \to \infty } } \left| {\hat \mu (t)} \right| \leqq 2\delta \)

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University of New Mexico
United States

Keywords

Characteristic functions; other transforms, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

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