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1.
涂天亮  邓继恩 《数学学报》2010,53(2):393-408
该文在Jordan区域上研究扰动Fejér点上Hermite--Fejér插值对的逼近阶与收敛性, 完全解决了美国数学会 1991年Transactions of the AMS中Chui和Shen提出的问题,并将其边界条件J2改进为.    相似文献   

2.
We consider inequalities of the Jackson type in the case of approximation of periodic functions by linear means of their Fourier series in the space L 2. In solving this problem, we choose the integral of the square of the modulus of continuity as a majorant of the square of the deviation. We establish that the constants for the Fejér and Rogosinski polynomials coincide with the constant of the best approximation, whereas the constant for the Korovkin polynomials is greater than the constant of the best approximation.  相似文献   

3.
Computational schemes for the collocation method and the mechanical quadrature method for the approximate solution of systems of singular integro-differential equations with a Cauchy kernel are elaborated. The case where the systems of equations are defined on an arbitrary smooth closed contour of a complex plane is examined. The methods researched are based on Fejér points. Estimates of the rate of convergence in Lebesgue space are obtained.  相似文献   

4.
A construction of Carathéodory and Fejér [1] produces a function which is bounded and analytic in the unit disk with specified initial coefficients. An operator generalization of the construction is now obtained for application to the invariant subspace problem. A formal proof [2] of the existence of invariant subspaces is given by the theory of square summable power series [3] in its vector formulation [4]. But the justification of the formal argument requires a determination of extreme points of a convex set [5]. A solution is now given to an extension problem for convex decompositions which arises in connection with the Carathéodory-Fejér theorem. A necessary condition for an extreme point is obtained as an application. The condition is conjectured to be sufficient.  相似文献   

5.
We obtain the best estimate for approximations of continuous 2-periodic functions by Fejér summation operators. The estimate is expressed in terms of the moduli of continuity of functions to be approximated. In the class of functions satisfying Lipschitz condition, we obtain the best constant for the approximation by Fejer integral and summation operators.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 1, pp. 75–82, 1990.  相似文献   

6.
Ohne ZusammenfassungAus einem Brief an Herrn L. Fejér.  相似文献   

7.
The solutions of the Carathéodory–Fejér interpolation problem for generalized Schur functions can be parametrized via a linear fractional transformation over the class of classical Schur functions. The linear fractional transformation of some of these functions may have a pole (simple or multiple) in one or more of the interpolation points or not satisfy one or more interpolation conditions, hence not all Schur functions can serve as a parameter. The set of excluded parameters is characterized in terms of the related Pick matrix.Research was supported by the Summer Research Grant from the College of William and MarySubmitted: June 26, 2002 Revised: January 31, 2003  相似文献   

8.
We propose a method for the approximation of analytic functionson Jordan regions that is based on a Carathéodory—Fejértype of economization of the Faber series. The method turnsout to be very effective if the boundary of the region is analytic.It often still works when the region degenerates to a Jordanarc. We also derive related lower and upper bounds for the errorof the best approximation. *Research carried out while this author was at ETH Zurich partiallysupported by a Royal Society European Visiting Fellowship.  相似文献   

9.
We show that the classical results of L.Fejér and M. Riesz concerning norm convergence of trigonometric Fourier series can be carried over to eigenfunction expansions arising from regular indefinite boundary eigenvalue problems.  相似文献   

10.
The discrete least squares method is convenient for computing polynomial approximations to functions. We investigate the possibility of using this method to obtain polynomial approximants good in the uniform norm, and find that for a given set ofm nodes, the degreen of the approximating polynomial should be selected so that there is a subset ofn+1 nodes which are close ton+1 Fejér points for the curve. Numerical examples are presented.Sponsored by the United States Army under Contract No. DAAG29-80-C-0041.  相似文献   

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