共查询到20条相似文献,搜索用时 46 毫秒
1.
The goal of the paper is to prove generalizations of the classical Plancherel–Polya inequalities in which point-wise sampling of functions (δ-distributions) is replaced by more general compactly supported distributions on . As an application it is shown that a function , 1p∞, which is an entire function of exponential type is uniquely determined by a set of numbers {Ψj(f)}, , where {Ψj}, , is a countable sequence of compactly supported distributions. In the case p=2 a reconstruction method of a Paley–Wiener function f from a sequence of samples {Ψj(f)}, , is given. This method is a generalization of the classical result of Duffin–Schaeffer about exponential frames on intervals. 相似文献
2.
Samir H. Saker Ravi P. Agarwal Donal O'Regan 《Journal of Mathematical Analysis and Applications》2007,330(2):1317-1337
The study of dynamic equations on time scales has been created in order to unify the study of differential and difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which may be an arbitrary closed subset of the reals. This way results not only related to the set of real numbers or set of integers but those pertaining to more general time scales are obtained. In this paper, by employing the Riccati transformation technique we will establish some oscillation criteria for second-order linear and nonlinear dynamic equations with damping terms on a time scale . Our results in the special case when and extend and improve some well-known oscillation results for second-order linear and nonlinear differential and difference equations and are essentially new on the time scales , h>0, for q>1, , etc. Some examples are considered to illustrate our main results. 相似文献
3.
Let be any atomless and countably additive probability measure on the product space with the usual σ-algebra. Then there is a purely finitely additive probability measure λ on the power set of a countable subset such that can be isometrically isomorphically embedded as a closed subspace of Lp(λ). The embedding is strict. It is also ‘canonical,’ in the sense that it maps simple and continuous functions on to their restrictions to T. 相似文献
4.
We consider the following nonlinear elliptic equation with singular nonlinearity: where α>β>1, a>0, and Ω is an open subset of , n2. Let uH1(Ω) with and be a nonnegative stationary solution. If we denote the zero set of u by we shall prove that the Hausdorff dimension of Σ is less than or equal to . 相似文献
5.
For any integers p,n≥2 necessary and sufficient conditions are given for scaling filters with pn many terms to generate a p-multiresolution analysis in . A method for constructing orthogonal compactly supported p-wavelets on is described. Also, an adaptive p-wavelet approximation in is considered. 相似文献
6.
The aim of this paper is to discuss the positive solutions of the p-Laplace problem
−div(|u|p−2u)+g(u)|u|p=λuq,