共查询到20条相似文献,搜索用时 9 毫秒
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Using the following notation: C is the space of continuous bounded functions f equipped with the norm
, V is the set of functions f such that
, the set E consists of fCV and possesses the following property:
is summable on each finite interval,
we establish some assertions similar to the following theorem: Let
0$$
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,
Then for fV the series
uniformly converges with respect to
and the following equality holds:
This theorem develops some results obtained by Zubov relative to the approximation of probability distributions. Bibliography: 4 titles. 相似文献
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In the space $C(\mathbb{R})$ , we construct special summation operators of Jackson type with rational kernels and under a suitable choice of poles we obtain order estimates for deviations of these operators from functions belonging to certain classes. 相似文献
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For a class of entire functions we study the problem of estimation of the order of growth of functions on the real axis. This problem is important for the justification of the integral representation of bounded solutions to certain partial differential equations considered in other papers of the authors. In order to obtain an estimate of the order of growth of a function on the real axis, we use the method of differential equations. The method is based, on one hand, on the construction of a system of first-order ordinary differential equations whose solution is a vector function of traces of function and its derivatives on the real axis. On the other hand, under the respective change of variables in the system of equations, we obtain an estimate of the solution to the system of equations for a large positive values of the argument. The obtained estimate is non-trivial and shows the way a complex parameter of a power series affects the order of growth of a function. 相似文献
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Approximation of Multivariate Functions with a Certain Mixed Smoothness by Entire Functions 总被引:2,自引:0,他引:2
ApproximationofMultivariateFunctionswith aCertainMixedSmoothnessbyEntireFunctionsWangHeping(汪和平);SunYongsheng(孙永生)(Department... 相似文献
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In this paper, we study the pointwise approximation of functions defined on the real semiaxis and having an rth derivative bounded almost everywhere. The approximation is performed by means of entire functions of bounded half-degree, which were introduced by S. N. Bernstein. An asymptotically sharp estimate for pointwise approximation of this class of functions is obtained. 相似文献
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我们研究了由仅有实零点的代数多项式导出的微分算子确定的广义Sobolev类利用指数型整函数作为逼近工具的最佳限制逼近问题.利用Fourier变换和周期化等方法,得到在L_2(R)范数下的广义Sobolev光滑函数类的相对平均宽度和最佳限制逼近的精确常数,以及当0是这个代数多项式的一个至多2重的零点时,得到最佳限制逼近在L_1(R)范数和一致范数下的广义Sobolev类的精确到阶的结果. 相似文献
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Ukrainian Mathematical Journal - We present a brief survey of works in the approximation theory of functions known to the author and connected with V. K. Dzyadyk’s research works. 相似文献
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N. A. Shirokov 《Journal of Mathematical Sciences》2004,124(2):4935-4939
Let
, where the
and
satisfy the following relations:
and
. Denote by B
the class of all entire functions of exponential type bounded on the real axis. Under certain assumptions on the rate of approximation on E of a bounded function f by functions in B
( varies), we get some information about the smoothness of f. Bibliography: 4 titles. 相似文献
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For two closed sets F and G in the complex plane C, G
C , we solve the following problem Under what conditions on F and G can every function f , continuous on F and analytic in its interior, be uniformly approximated by entire functions, each of which is bounded on G ?
February 7, 1995. Date revised: October 31, 1995. 相似文献
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In the present paper, we study the polynomial approximation of entire functions of several complex variables. The characterizations of generalized order and generalized type of entire functions of slow growth are obtained in terms of approximation and interpolation errors. 相似文献
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《复变函数与椭圆型方程》2012,57(6):527-542
In this article, we discuss the Riemann boundary value problems and the Hilbert boundary value problems of polyanalytic functions on the real axis, and both the explicit expressions of solutions and the conditions of solvability are obtained. 相似文献
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Ukrainian Mathematical Journal - The title of the article should read: Approximation by Interpolation Trigonometric Polynomials in Metrics of the Space Lp on the Classes of Periodic Entire... 相似文献
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Wolfgang Gehlen 《Journal of Approximation Theory》1998,94(3):467-480
We consider the distribution of alternation points in best real polynomial approximation of a functionf∈C[−1, 1]. For entire functionsfwe look for structural properties of f that will imply asymptotic equidistribution of the corresponding alternation points. 相似文献
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Ukrainian Mathematical Journal - We establish asymptotic equalities for the least upper bounds of approximations by interpolation trigonometric polynomials with equidistant distribution of... 相似文献