On the Absolute Continuity of Gaussian Measures on Locally Compact Groups

This note discusses the topological necessary and sufficient conditions for a locally compact connected group to admit a Gaussian measure that is absolutely continuous with respect to Haar measure.     

Approximation of functions of boundedp-variation by polynomials in terms of the faber-schauder system

In this paper the best polynomial approximation in terms of the system of Faber-Schauder functions in the spaceC _p [0, 1] is studied. The constant in the estimate of Jackson’s inequality for the best approximation in the metric ofC _p [0, 1] and the estimate of the modulus of continuity ω_1−1/p are refined. Translated fromMatematicheskie Zametki, Vol. 62, No. 3, pp. 363–371, September, 1997. Translated by N. K. Kulman     

含随机相位的余弦波过程在Haar小波下的性质

利用随机过程的小波变换，研究了含有随机相位的余弦过程在Haar小波下的统计性质.     

Fractal Haar system

The Haar system is an alternative to the classical Fourier bases, being particularly useful for the approximation of discontinuities. The article tackles the construction of a set of fractal functions close to the Haar set. The new system holds the property of constitution of bases of the Lebesgue spaces of p-integrable functions on compact intervals. Likewise, the associated fractal series of a continuous function is uniformly convergent. The case p=2 owns some peculiarities and is studied separately.     

基于无抽取Haar算法的实时卡尔曼滤波方法

针对基于分段方式的多尺度卡尔曼滤波其计算量大、延时长的问题,提出基于无抽取Haar算法的实时卡尔曼滤波方法,该方法采用简单的加减、移位运算在t时刻完成多尺度变换,然后在各个尺度进行小波阈值去噪和卡尔曼滤波;为了验证该方法的有效性,在自主改装的智能车上对低精度加速度传感器进行实验.研究结果表明:通过小波重构完成信号处理,提高了算法实时性,并且有效减少重复运算;实时卡尔曼滤波方法有效提高了传感器的性能,在不能准确估计状态转移误差情况下,该方法的去噪性能优于单独的卡尔曼滤波去噪性能.     

Degenerate kernel schemes by wavelets for nonlinear integral equations on the real line

A degenerate kernel scheme is developed for nonlinear integral equations on the real line by approximation of kernels by wavelets. The rate of convergence of the approximate solutions is established in terms of the decay rate of the kernels andthe numbers of dilations and shifts used in approximation of the kernels. For linear equations, the Haar wavelet approximation is used and a numerical example is included.     

NORMALLY DISTRIBUTED PROBABILITY MEASURE ON THE METRIC SPACE OF NORMS

In this paper we propose a method to construct probability measures on the space of convex bodies. For this purpose, first, we introduce the notion of thinness of a body. Then we show the existence of ...