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991.
Gaurav Thakur 《Journal of Functional Analysis》2011,260(8):2283-2299
We study some problems related to the effect of bounded, additive sample noise in the bandlimited interpolation given by the Whittaker-Shannon-Kotelnikov (WSK) sampling formula. We establish a generalized form of the WSK series that allows us to consider the bandlimited interpolation of any bounded sequence at the zeros of a sine-type function. The main result of the paper is that if the samples in this series consist of independent, uniformly distributed random variables, then the resulting bandlimited interpolation almost surely has a bounded global average. In this context, we also explore the related notion of a bandlimited function with bounded mean oscillation. We prove some properties of such functions, and in particular, we show that they are either bounded or have unbounded samples at any positive sampling rate. We also discuss a few concrete examples of functions that demonstrate these properties. 相似文献
992.
In this paper we study the maximal operators and the convolution operators Tδ associated with multipliers of the form
993.
We consider generalized potential operators with the kernel on bounded quasimetric measure space (X, μ, d) with doubling measure μ satisfying the upper growth condition μB(x, r) ? KrN, N ∈ (0, ∞). Under some natural assumptions on a(r) in terms of almost monotonicity we prove that such potential operators are bounded from the variable exponent Lebesgue space Lp(?)(X, μ) into a certain Musielak‐Orlicz space Lp(X, μ) with the N‐function Φ(x, r) defined by the exponent p(x) and the function a(r). A reformulation of the obtained result in terms of the Matuszewska‐Orlicz indices of the function a(r) is also given. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
994.
A normalized univalent function f is called Ma-Minda starlike or convex if zf′(z)/f(z)?φ(z) or 1+zf″(z)/f′(z)?φ(z) where φ is a convex univalent function with φ(0)=1. The class of Ma-Minda convex functions is shown to be closed under certain operators that are generalizations of previously studied operators. Analogous inclusion results are also obtained for subclasses of starlike and close-to-convex functions. Connections with various earlier works are made. 相似文献
995.
996.
In the present paper, we consider the classical Widder transform, the Hν-transform, the Kν-transform, and the Yν-transform. Some identities involving these transforms and many others are given. By making use of these identities, a number of new Parseval-Goldstein type identities are obtained for these and other well-known integral transforms. 相似文献
997.
Zheng Liu 《Applied mathematics and computation》2011,218(4):1389-1398
A generalization of the corrected averaged midpoint-trapezoid rule is derived. Various error bounds for this generalization are established. 相似文献
998.
T. A. Mel'nyk Iu. A. Nakvasiuk W. L. Wendland 《Mathematical Methods in the Applied Sciences》2011,34(7):758-775
We consider a mixed boundary‐value problem for the Poisson equation in a thick junction Ωε which is the union of a domain Ω0 and a large number of ε—periodically situated thin cylinders. The non‐uniform Signorini conditions are given on the lateral surfaces of the cylinders. The asymptotic analysis of this problem is done as ε→0, i.e. when the number of the thin cylinders infinitely increases and their thickness tends to zero. We prove a convergence theorem and show that the non‐uniform Signorini boundary conditions are transformed in the limiting variational inequalities in the region that is filled up by the thin cylinders as ε→0. The convergence of the energy integrals is proved as well. The existence and uniqueness of the solution to this non‐standard limit problem is established. This solution can be constructed by using a penalty formulation and successive iteration. For some subclass, these problems can be reduced to an obstacle problem in Ω0 and an appropriate postprocessing. The equations in Ω0 finally are also treated with boundary integral equations. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
999.
Veli SHAKHMUROV 《数学年刊B辑(英文版)》2011,32(5):749-770
The free boundary value problems for elliptic differential-operator equations are studied. Several conditions for the uniform
maximal regularity with respect to boundary parameters and the Fredholmness in abstract L
p
-spaces are given. In application, the nonlocal free boundary problems for finite or infinite systems of elliptic and anisotropic
type equations are studied. 相似文献
1000.
We prove that the octonionic polynomials V ■k l 1 ··· l k are independent of the associative orders ■k . This improves the octonionic Taylor type theorem. 相似文献