Geodesic
A law of the iterated logarithm for general lacunary series
Charles N. Moore 1   ; Xiaojing Zhang 1
1 Department of Mathematics Kansas State University Manhattan, KS 66506, U.S.A.
Colloquium Mathematicum, Tome 126 (2012) no. 1, pp. 95-103 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We prove a law of the iterated logarithm for sums of the form $\sum_{k=1}^N a_k f(n_k x)$ where the $n_k$ satisfy a Hadamard gap condition. Here we assume that $f$ is a Dini continuous function on $\mathbb R^n$ which has the property that for every cube $Q$ of sidelength 1 with corners in the lattice $\mathbb Z^n$, $f$ vanishes on $\partial Q$ and has mean value zero on $Q.$
DOI : 10.4064/cm126-1-6
Keywords: prove law iterated logarithm sums form sum f where satisfy hadamard gap condition here assume dini continuous function mathbb which has property every cube sidelength corners lattice mathbb vanishes partial has mean value zero nbsp

Charles N. Moore  1   ; Xiaojing Zhang  1

1 Department of Mathematics Kansas State University Manhattan, KS 66506, U.S.A. 
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Charles N. Moore; Xiaojing Zhang. A law of the iterated logarithm for general lacunary series. Colloquium Mathematicum, Tome 126 (2012) no. 1, pp. 95-103. doi: 10.4064/cm126-1-6

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