共查询到20条相似文献,搜索用时 0 毫秒
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We consider the problem of representing elements of a weighted space of infinitely differentiable functions on the real line by series of exponentials. 相似文献
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We study approximation problems for infinitely differentiable multivariate functions in the worst-case setting. Using a series of information-based algorithms as approximation tools, in which each algorithm is constructed by performing finitely many standard information operations, we prove that the L∞-approximation problem is exponentially convergent. As a corollary, we show that the corresponding integral problem is exponentially convergent as well. 相似文献
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本文研究\,$[-1,1]$上的一个无限可微函数类$F_\infty$在空间$L_\infty[-1,1]$及加权空间$L_{p,\omega}[-1,1]$, $1\le p< \infty$ ($\omega$是$(-1,1)$上的非负连续可积函数)的最优Lagrange插值.我们证明了基于首项系数为1且于$L_{p,\omega}[-1,1]$上有最小范数的多项式零点的Lagrange插值对$1\le p< \infty$是最优的. 同时我们给出了当结点组包含端点时的最优结点组. 相似文献
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We consider questions of rational and polynomial approximation,and related extension questions, for various normed spaces ofinfinitely differentiable functions on perfect compact subsetsof the complex plane C and the real line R. We obtain an approximationtheorem for compact planar sets which are, in a precise sense,locally radially self-absorbing. All smoothly-bounded compactsets are of this type. We give a variety of results and counterexampleson extension, mainly in the one-dimensional case. We also provepolynomial approximation theorems for totally-disconnected sets,linear sets, and some others. 相似文献
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We present a sufficient condition for the surjectivity of a linear differential operator of infinite order with constant coefficients in a weighted space of infinitely differentiable functions on the real line. 相似文献
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R. Horst 《The Journal of the Operational Research Society》1981,32(9):821-824
By very elementary arguments on Lagrangian duality it is shown that the classical resource allocation problem can be reduced to a single one-dimensional minimization of a differentiable convex function. An optimality condition is given that can be used for testing optimality of some proposed heuristic solutions. 相似文献
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A. A. Mogul’skiĭ 《Siberian Advances in Mathematics》2018,28(1):65-73
For a pair of convex lower semicontinuous functions connected by the Legendre transform, we establish that their derivatives are mutually inverse functions (in the generalized sense). 相似文献
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We obtain asymptotic equalities for the upper bounds of approximations of periodic infinitely differentiable functions by interpolation trigonometric polynomials in the metric of L1 on the classes of convolutions. 相似文献
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Let F
p,t
(n) denote the number of the coefficients of (x
1+1x
2+...+x
t
)
j
, 0 ≤j≤n− 1, which are not divisible by the prime p. Define G
p,t
(n) = F
p,t
/n
θ and β(p,t) = lim infF
p,t
)(n)/n
θ, where θ = (log)/(log p). In this paper, we mainly prove that G
p,t
can be extended to a continuous function on ℝ+, and the function G
p,t
is nowhere monotonic. Both the set of differential points of the function G
p,t
and the set of non-differential points of the function G
p,t
are dense in ℝ+.
Received February 18, 2000, Accepted December 7, 2000 相似文献
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In this paper, we generalize Bernstein's theorem characterizing the space
by means of local approximations. The closed interval
is partitioned into disjoint half-intervals on which best approximation polynomials of degree
divided by the lengths of these half-intervals taken to the power
are considered. The existence of the limits of these ratios as the lengths of the half-intervals tend to zero is a criterion for the existence of the
th derivative of a function. We prove the theorem in a stronger form and extend it to the spaces
. 相似文献
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P. J. de Paepe 《Czechoslovak Mathematical Journal》2003,53(1):77-81
Examples of non-finitely generated function algebras on planar sets with small maximal ideal spaces are given. 相似文献
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研究了高阶线性微分方程f~(k)+A_(k-1)(z)f~(k-1)+…+A_1(z)f′+A_0(z)f=0的非零解f,及其一阶、二阶导数,f~(i)(i=1,2)的不动点性质,这里A_j(z)(j=0,1,…k-1)为亚纯函数,得到了若δ(∞,A_0)>0,且满足max{i(A1),i(A2),…,i(A_(k-1))}相似文献