Continued fraction Cantor sets, Hausdorff dimension, and functional analysis
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For n N, the sets En consist of all (0, 1) whose continued fraction expansion involves only partial quotients n. They are fractal subsets of (0, 1) with Hausdorff dimension, dim(En), between 0 and 1. Analysis of the related linear operators Ls,nf(t):= k=1 n(k+t)-sf( 1 (k+t)) acting on a certain space B of functions on (0, 1), yields information about dim(En). The main result is that as n , dim(En)=1- 6 2n-72log n 4n2+O( 1 n2). 1992.
