共查询到20条相似文献,搜索用时 31 毫秒
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Let 0≤g be a dyadic Hölder continuous function with period 1 and g(0)=1, and let $G(x) = \prod\nolimits_{n = 0}^\infty {g(x/{\text{2}}^n )} $ . In this article we investigate the asymptotic behavior of $\smallint _0^{\rm T} \left| {G(x)} \right|^q dx$ and $\frac{1}{n}\sum\nolimits_{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 regulatiry of wavelets and Bernoulli convolutions. 相似文献
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On convergence of the averages\frac{1}{N}\sum\nolimits_{n = 1}^N {f_1 (R^n x)f_2 (S^n x)f_3 (T^n x)}
Qing Zhang 《Monatshefte für Mathematik》1996,122(3):275-300
In this note, we will prove that for commuting ergodic measure preserving transformationsR, S andT, ifRT ?1,ST ?1 are also ergodic, then the limit $$\lim \frac{1}{N}\sum\nolimits_{n = 1}^N {f_1 (R^n x)f_2 (S^n x)f_3 (T^n x)} $$ exists inL 1-norm. The method used in this note was developed byConze, Furstenberg, Lesigne andWeiss. 相似文献
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Periodica Mathematica Hungarica - We consider the functional equation $$G\left( x,G\left( y,x\right) \right) =G\left( y,G\left( x,y\right) \right) $$, posed in Jarczyk and Jarczyk (Aequ Math... 相似文献
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J. O. C. Ezeilo 《Annali di Matematica Pura ed Applicata》1968,80(1):281-299
Summary In this paper my previous result [1] on the boundedness of solutions of (1.1.1) is fackled by use of a suitably chosen Liapounov
function. This fresh approach leads to a more direct proof of the boundedness Theorem and makes for substantial reduction
in each of my previous conditions on f and g. 相似文献
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Let p(n) denote the partition function and let \(\Delta \) be the difference operator with respect to n. In this paper, we obtain a lower bound for \(\Delta ^2\log \root n-1 \of {p(n-1)/(n-1)}\), leading to a proof of a conjecture of Sun on the log-convexity of \(\{\root n \of {p(n)/n}\}_{n\ge 60}\). Using the same argument, it can be shown that for any real number \(\alpha \), there exists an integer \(n(\alpha )\) such that the sequence \(\{\root n \of {p(n)/n^{\alpha }}\}_{n\ge n(\alpha )}\) is log-convex. Moreover, we show that \(\lim \limits _{n \rightarrow +\infty }n^{\frac{5}{2}}\Delta ^2\log \root n \of {p(n)}=3\pi /\sqrt{24}\). Finally, by finding an upper bound for \(\Delta ^2 \log \root n-1 \of {p(n-1)}\), we establish an inequality on the ratio \(\frac{\root n-1 \of {p(n-1)}}{\root n \of {p(n)}}\). 相似文献
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Aequationes mathematicae - 相似文献