Asymptotic Behavior of Multiperiodic Functions
Aihua Fan, Ka‐Sing Lau, Robert S. Strichartz · 1998
Let 0 < g be a dyadic H61der continuous function with period 1 and g(O) = i, and let G(x) = I-IT=0 g (x/2n). In this article we investigate the asymptotic behavior of fo T (G(x)lqdx and 1 n ~k=0 log g(2k x ) using the dynamical system techniques: the pressure function and the variational principle. An algorithm to calculate the pressure is presented. The results are applied to study the regularity of wavelets and Bernoulli convolutions.