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51.
The paper gives first quantitative estimates on the modulus of continuity of the spectral measure for weak mixing suspension flows over substitution automorphisms, which yield information about the “fractal” structure of these measures. The main results are, first, a Hölder estimate for the spectral measure of almost all suspension flows with a piecewise constant roof function; second, a log-Hölder estimate for self-similar suspension flows; and, third, a Hölder asymptotic expansion of the spectral measure at zero for such flows. Our second result implies log-Hölder estimates for the spectral measures of translation flows along stable foliations of pseudo-Anosov automorphisms. A key technical tool in the proof of the second result is an “arithmetic-Diophantine” proposition, which has other applications. In Appendix A this proposition is used to derive new decay estimates for the Fourier transforms of Bernoulli convolutions. 相似文献
52.
We expand upon the known results on sharp linear Fourier methods of approximation where the approximation is the best in terms of both rate and constant among all polynomial procedures of approximation. So far these results have been studied due to their mathematical beauty rather than their practical importance. In this paper we show that they are the core mathematics underlying best statistical methods of solving noisy ill-posed problems. In particular, we suggest a procedure for recovery of noisy blurred signals based on samples of small sizes where a traditional statistics concludes that the complexity of such a setting makes the problem not worthy of a further study. Thus, we present a problem where a combination of the classical approximation theory and statistics leads to interesting practical results. 相似文献
53.
54.
强奇异卷积算子交换子的Hardy型空间估计 总被引:2,自引:0,他引:2
本文给出了强奇异卷积算子交换子[6,T]在Hardy型空间中的估计,其中 b∈BMO(Rn)且一致连续, T为强奇异卷积算子. 相似文献
55.
Let Φ′ be the strong dual of a nuclear Fréchet space Φ. In this paper we present regularity properties, weak convergence, and convergence in probability and in mean square of Φ′-valued stochastic evolution equations and convolutions with respect to Φ′-valued cadlag martingales. 相似文献
56.
David M. Bradley Ramesh C. Gupta 《Annals of the Institute of Statistical Mathematics》2002,54(3):689-700
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the characteristic function, we derive explicit formulae for the distribution of the sum of n non-identically distributed uniform random variables in both the continuous and the discrete case. The results, though involved, have a certain elegance. As examples, we derive from our general formulae some special cases which have appeared in the literature. 相似文献
57.
Josefina Alvarez Martha Guzmn-Partida 《Journal of Mathematical Analysis and Applications》2002,270(2):235-434
We characterize those tempered distributions which are S′-convolvable with a given class of singular convolution kernels. We study both, the Euclidean case and the product domain case. In the Euclidean case, we consider a class of kernels that includes Riesz kernels, Calderón–Zygmund singular convolution kernels, finite part distributions defined by hypersingular convolution kernels, and Hörmander multipliers. In the product domain case, we consider a class of singular kernels introduced by Fefferman and Stein as a generalization of the n-dimensional Hilbert kernel. 相似文献
58.
59.
二维卷积及其在色谱峰纯度鉴定中的应用 总被引:2,自引:0,他引:2
光电二极管阵列检测器与色谱仪的联用 ( HPLC- DAD)为复杂体系中多组分的定性定量分析提供了可能 .Savitzky等 [1]提出了以简单的卷积运算完成数值微分方法 .Gorry等 [2 ]曾以 Gram正交多项式替代幂级数拟合 ,让卷积技术可以覆盖到谱图包括起讫部分的任一点 .Edwards[3]与 Kuo[4 ]等提出的二维卷积法对处理和利用二变量数据矩阵具有普遍意义 ,但理论推导繁琐 .我们曾完善了推求二维卷积整数的普遍方法 [5] ,并研究和解决了一维和二维卷积中的信息丢失问题 [6 ,7] .本文提出了一种简化的求算二维卷积整数的方法 .理论推导表明 ,二维卷积… 相似文献
60.
Randomization time for the overhand shuffle 总被引:1,自引:0,他引:1
Robin Pemantle 《Journal of Theoretical Probability》1989,2(1):37-49
This paper analyzes repeated shuffling of a deck ofN cards. The measure studied is a model for the popularoverhand shuffle introduced by Aldous and Diaconis. It is shown that convergence to the uniform distribution requires at least orderN
2 shuffles, and that orderN
2 log(N) shuffles suffice. For a 52-card deck, more than 1000 shuffles are needed. 相似文献