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The Perron-Frobenius operator on BV. I. (English) Zbl 1084.11506

Summary: In this paper, we determine the upper bound \(\gamma_n\) of \(\text{var}\,U^n f/\text{var}\,f\), when \(f\) varies in the collection of non-constant monotone functions on \(I=[0,1]\).

MSC:

11K50 Metric theory of continued fractions
37A45 Relations of ergodic theory with number theory and harmonic analysis (MSC2010)
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