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11.
Wengu Chen Yixin Lai 《分析论及其应用》2006,22(2):195-200
Let μ be a Borel measure on Rd which may be non doubling. The only condition that μ must satisfy is μ(Q) ≤ col(Q)n for any cube Q () Rd with sides parallel to the coordinate axes and for some fixed n with 0 < n ≤ d. The purpose of this paper is to obtain a boundedness property of fractional integrals in Hardy spaces H1 (μ). 相似文献
12.
13.
We study a class of ‘nonpoissonian’ transformations of the configuration space and the corresponding transformations of the Poisson measure. For some class of Poisson measures we find conditions which are sufficient for the transformed measure (which in general is nonpoissonian) to be absolutely continuous with respect to the initial Poisson measure and get the expression for the corresponding Radon–Nikodym derivative. To solve this problem we use a distributional approach to Poisson multiple stochastic integrals. 相似文献
14.
本将小波分析方法用于一类奇异积分方程的计算,建立了小波展开的非标准形式与标准形式转换关系,根据Mallat小波快速算法,设计了此类积分的计算算法,并通过实际例子验证了方法的有效性,计算具有速度快,运算量少的特点。 相似文献
15.
In this article, we solve in closed form a system of nonlinear differential equations modelling the elastica in space of a thin, flexible, straight rod, loaded by a constant thrust at its free end. Common linearizations of strength of materials are of course not applicable any way, because we analyze great deformations, even if not so large to go off the linear elasticity range. By passing to cylindrical coordinates ρ, θ, z, we earn a more tractable differential system evaluating ρ as elliptic function of polar anomaly θ and also providing z through elliptic integrals of I and III kind. Deformed rod’s centerline is then completely described under both tensile or compressive load. Finally, the planar case comes out as a degeneracy, where the Bernoulli lemniscatic integral appears. 相似文献
16.
Suppose that the signal X to be estimated is a diffusion process in a random medium W and the signal is correlated with the observation noise. We study the historical filtering problem concerned with estimating the signal path up until the current time based upon the back observations. Using Dirichlet form theory, we introduce a filtering model for general rough signal X
W
and establish a multiple Wiener integrals representation for the unnormalized pathspace filtering process. Then, we construct a precise nonlinear filtering model for the process X itself and give the corresponding Wiener chaos decomposition. 相似文献
17.
18.
We first state a uniform convergence theorem for finite-part integrals which are derivatives of weighted Cauchy principal value integrals. We then give a two-stage process to modify approximating splines and optimal nodal splines in such a way that the conditions of this theorem are satisfied. Consequently, these modified splines can be used in the numerical evaluation of these finite-part integrals. 相似文献
19.
In this paper cubature formulas based on bivariate C
1 local polynomial splines with a four directional mesh [4] are generated and studied. Some numerical results with comparison
with other methods are given. Moreover the method proposed is applied to the numerical evaluation of 2‐D singular integrals
defined in the Hadamard finite part sense. Computational features, convergence properties and error bounds are proved.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
20.
Katsuhisa Mimachi 《Compositio Mathematica》1998,113(2):117-122
We give a short proof of the inner product conjecture for the symmetric Macdonald polynomials of type An-1. As a special case, the corresponding constant term conjecture is also proved. 相似文献