Continued fraction Cantor sets, Hausdorff dimension, and functional analysis Academic Article uri icon

abstract

  • For n ∈ N, the sets En consist of all α ∈ (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 π2n-72log n π4n2+O( 1 n2). © 1992.

author list (cited authors)

  • Hensley, D.

citation count

  • 43

publication date

  • March 1992