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71.
We study the approximation of the inverse wavelet transform using Riemannian sums.We show that when the Fourier transforms of wavelet functions satisfy some moderate decay condition,the Riemannian sums converge to the function to be reconstructed as the sampling density tends to infinity.We also study the convergence of the operators introduced by the Riemannian sums.Our result improves some known ones. 相似文献
72.
Arzhang AngoshtariArash Yavari 《Physics letters. A》2011,375(10):1281-1285
A rigorous proof for convergence of the Wolf method (Wolf et al., 1999 [9]) for calculating electrostatic energy of a periodic lattice is presented. In particular, we show that for an arbitrary lattice of unit cells, the lattice sum obtained via Wolf method converges to the one obtained via Ewald method. 相似文献
73.
Several authors have studied the uniform estimate for the tail probabilities of randomly weighted sumsa.ud their maxima. In this paper, we generalize their work to the situation thatis a sequence of upper tail asymptotically independent random variables with common distribution from the is a sequence of nonnegative random variables, independent of and satisfying some regular conditions. Moreover. no additional assumption is required on the dependence structureof {θi,i≥ 1). 相似文献
74.
Let {X,X_k:k≥1} be a sequence of extended negatively dependent random variables with a common distribution F satisfying EX 0.Let r be a nonnegative integer-valued random variable,independent of {X,X_k:k≥1}.In this paper,the authors obtain the necessary and sufficient conditions for the random sums S_r =(?)X_n to have a consistently varying tail when the random number t has a heavier tail than the summands,i.e.,(P(Xx))/(P(r x))→0as x→∞ 相似文献
75.
76.
77.
We show that for any mod 2m characters, χ1, χ2, the complete exponential sum,∑~(2m)_(x=1)χ1(x)χ2(Ax~k+ B) has a simple explicit evaluation. 相似文献
78.
79.
Let X1, …, Xn be independent random variables and define for each finite subset I {1, …, n} the σ-algebra
= σ{Xi : i ε I}. In this paper
-measurable random variables WI are considered, subject to the centering condition E(WI
) = 0 a.s. unless I J. A central limit theorem is proven for d-homogeneous sums W(n) = ΣI = dWI, with var W(n) = 1, where the summation extends over all (nd) subsets I {1, …, n} of size I = d, under the condition that the normed fourth moment of W(n) tends to 3. Under some extra conditions the condition is also necessary. 相似文献
80.
David Borwein Jonathan M. Borwein David M. Bradley 《Journal of Mathematical Analysis and Applications》2006,316(1):328-338
We consider some parametrized classes of multiple sums first studied by Euler. Identities between meromorphic functions of one or more variables in many cases account for reduction formulae for these sums. 相似文献