共查询到20条相似文献,搜索用时 30 毫秒
1.
Péter Kórus 《Czechoslovak Mathematical Journal》2018,68(4):987-996
We extend the results of paper of F.Móricz (2010), where necessary conditions were given for the L1-convergence of double Fourier series. We also give necessary and sufficient conditions for the L1-convergence under appropriate assumptions. 相似文献
2.
Allan Pinkus 《Constructive Approximation》1988,4(1):85-96
C 1(K) is the space of real continuous functions onK endowed with the usualL 1,-norm where \(K = \overline {\operatorname{int} K}\) is compact inR m · U is a finite-dimensional subspace ofC 1,(K). The metric projection ofC 1,(K) ontoU contains a continuous selection with respect toL 1, -convergence if and only ifU is a unicity (Chebyshev) space forC 1,(K). Furthermore, ifK is connected andU is not a unicity space forC 1,(K), then there is no continuous selection with respect toL ∞-convergence. An example is given of aU and a disconnectedK with no continuous selection with respect toL 1-convergence, but many continuous selections with respect toL ∞-convergence. 相似文献
3.
We study homogenization by ??-convergence, with respect to the L 1-strong convergence, of periodic multiple integrals in W 1,?? when the integrand can take infinite values outside of a convex bounded open set of matrices. 相似文献
4.
The aim of the paper is to prove optimal results on local and global uniform convergence of solutions to elliptic equations with Dirichlet boundary conditions on varying domains. We assume that the limit domain be stable in the sense of Keldyš [Amer. Math. Soc. Transl. 51 (1966) 1-73]. We further assume that the approaching domains satisfy a necessary condition in the inside of the limit domain, and only require L2-convergence outside. As a consequence, uniform and L2-convergence are the same in the trivial case of homogenisation of a perforated domain. We are also able to deal with certain cracking domains. 相似文献
5.
《Statistics & probability letters》1997,32(2):147-159
We prove uniform L2-convergence of local times of aperiodic recurrent random walks to local times of strictly α-stable processes with α > 1. 相似文献
6.
We study here L1-convergence of new modified double cosine trigonometric sum and obtain a new necessary and sufficient condition for L1-convergence of double cosine trigonometric series.Also,the results obtained by Moricz[1],[2] are particular cases of ours. 相似文献
7.
We continue to investigate the application of the Mean Value Bounded Variation (MVBV) concept in real sense, and prove the necessary and sufficient condition for L 1-convergence of trigonometric series. 相似文献
8.
In this paper we obtain a necessary and sufficient condition for the sine series with generalized quasi-convex coefficients to be a Fourier series. Also we studyL 1-convergence of this series under the said condition on the coefficients. 相似文献
9.
N. Tanovi?-Miller 《Journal of Mathematical Analysis and Applications》2003,284(1):351-372
New integrability and L1-convergence classes for the r-times differentiated trigonometric series are derived using known results on integrability and L1-convergence of trigonometric series. These classes, Theorems 1 and 2, subsume all known integrability and L1-convergence classes for differentiated series. In particular, the extensions of the Fomin type theorems to r-times differentiated series, due to S.S. Bhatia and B. Ram (Proc. Amer. Math. Soc. 124 (1996) 1821-1829) and S.Y. Sheng (Proc. Amer. Math. Soc. 110 (1990) 895-904), are deduced from our Theorem 2 and its corollary Theorem 4. Another extension of the known results for differentiated series is given in Theorem 6. This result is proved using Fomin's theorem on cosine and sine series (Mat. Zametki 23 (1978) 213-222), and as a corollary of Theorem 2. The first proof yields another interesting conclusion, namely that the Fomin type theorems for differentiated series can be deduced as consequences of the original Fomin's results. 相似文献
10.
Let {X n , n ≥ 1} be a sequence of negatively associated random variables. The aim of this paper is to establish some limit theorems of negatively associated sequence, which include the L p -convergence theorem and Marcinkiewicz–Zygmund strong law of large numbers. Furthermore, we consider the strong law of sums of order statistics, which are sampled from negatively associated random variables. 相似文献
11.
We characterize the relaxation of the perimeter in an infinite dimensional Wiener space, with respect to the weak L2-topology. We also show that the rescaled Allen–Cahn functionals approximate this relaxed functional in the sense of Γ-convergence. 相似文献
12.
V. A. Malyshev 《Journal of Mathematical Sciences》1998,92(1):3622-3629
In the form of nonlinear norm estimates, a quantitative refinement of the following fact is given: for n-convex functions
L1-convergence implies Cn−2-convergence. Bibliography: 2 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 232, 1996, pp. 123–133.
Translated by I. A. Fedortsova. 相似文献
13.
ZhenHuan Teng 《纯数学与应用数学通讯》1998,51(8):857-895
We derive a first-order rate of L1-convergence for stiff relaxation approximations to its equilibrium solutions, i.e., piecewise smooth entropy solutions with finitely many discontinuities for scalar, convex conservation laws. The piecewise smooth solutions include initial central rarefaction waves, initial shocks, possible spontaneous formation of shocks in a future time, and interactions of all these patterns. A rigorous analysis shows that the relaxation approximations to approach the piecewise smooth entropy solutions have L1-error bound of O(ε|log ε| + ε), where ε is the stiff relaxation coefficient. The first-order L1-convergence rate is an improvement on the error bound. If neither central rarefaction waves nor spontaneous shocks occur, the error bound is improved to O(ε). © 1998 John Wiley & Sons, Inc. 相似文献
14.
László Leindler 《Analysis Mathematica》2012,38(2):123-133
Our aim is to find the source why the logarithm sequences play the crucial role in the L 1-convergence of sine series. We define three new classes of sequences; one of them has the character of the logarithm sequences, the other two are the extensions of the class defined by Zhou and named Logarithm Rest Bounded Variation Sequences. In terms of these classes, extended analogues of Zhou??s theorems are proved. 相似文献
15.
Chen Mufa 《数学学报(英文版)》1991,7(1):19-37
This paper deals with the exponentialL
2-convergence for jump processes. We introduce some reduction methods and improve some previous results. Then we prove that
for birth-death processes, exponentialL
2-convergence coincides indeed with exponential ergodicity which is widely studied in the Markov chain theory.
Research supported in part by the National Natural Science Foundation of China and Fok Ying-Tung Educational Foundation 相似文献
16.
Lamberto Cesari 《Rendiconti del Circolo Matematico di Palermo》1990,39(2):169-209
We continue here the discussion on the existence of discontinuousBV minima, for a class of multiple integrals of the calculus of variationsI, we have started in [2] in view of possible studies on hyperbolic partial differential equations. Besides the associated Serrin integralJ, based onL 1-convergence, we take into consideration a modified Serrin-type functionalJ *. This new integralJ * will be needed in [3] to prove Rankine-Hugoniot type properties. 相似文献
17.
We develop the Euler–Maruyama scheme for a class of stochastic differential equations with Markovian switching (SDEwMSs) under non-Lipschitz conditions . Both L1 and L2-convergence are discussed under different non-Lipschitz conditions. To overcome the mathematical difficulties arisen from the Markovian switching as well as the non-Lipschitz coefficients, several new analytical techniques have been developed in this paper which should prove to be very useful in the numerical analysis of stochastic systems. 相似文献
18.
S. Fridli 《Journal of Mathematical Analysis and Applications》1997,210(2):731
In this paper we give a condition with respect to Walsh–Fourier coefficients that implies theL1-convergence of the corresponding Walsh–Fourier series. We show that theL1-convergence class induced by this condition contains each one of the previously known convergence classes as a proper subset. We also show that our condition implies not only theL1-convergence but also the convergence in the dyadic Hardy norm if the function represented by the series belongs to the dyadic Hardy space. 相似文献
19.
Min Guohua 《分析论及其应用》1992,8(3):28-37
In this paper, the Lp-convergence of Grünwald interpolation Gn(f,x) based on the zeros of Jacobi polynomials J
n
(α,β)
(x)(−1<α,β<1) is considered. Lp-convergence (0<p<2) of Grünwald interpolation Gn(f,x) is proved for p·Max(α,β)<1. Moreover, Lp-convergence (p>0) of Gn(f,x) is obtained for −1<α,β≤0. Therefore, the results of [1] and [3–5] are improved. 相似文献
20.
L. N. Galoyan 《Russian Mathematics (Iz VUZ)》2016,60(2):19-24
For sine and cosine Fourier serieswithmonotonic coefficients we study Lp-convergence (1 < p < ∞) of their Cesàro means of a negative order. 相似文献