ASYMPTOTIC-BEHAVIOR OF MULTIPERIODIC FUNCTIONS G(X)=PI(INFINITY)(N=1)G(X 2(N))/

Authors
FAN AH LAU KS
Citation
Ah. Fan et Ks. Lau, ASYMPTOTIC-BEHAVIOR OF MULTIPERIODIC FUNCTIONS G(X)=PI(INFINITY)(N=1)G(X 2(N))/, The journal of fourier analysis and applications, 4(2), 1998, pp. 129-150
Citations number
28
Categorie Soggetti
Mathematics,Mathematics
Journal title
The journal of fourier analysis and applications → ACNP
ISSN journal
10695869
Volume
4
Issue
2
Year of publication
1998
Pages
129 - 150
Database
ISI
SICI code
1069-5869(1998)4:2<129:AOMFG>2.0.ZU;2-E
Abstract
Let 0 less than or equal to g be a dyadic Holder continuous function w ith period 1 and g(0) = 1, and lei G(x) = Pi(n=0)(infinity)g(x/2(n)). In this article we investigate the asymptotic behavior of integral(0)( T) \G(x)\(q)dx and 1/n Sigma(k=0)(n) log g(2(k)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 convolution s.