三角多项式算子在BroWnian桥测度下的平均误差

The Average Errors for Trigonometric Polynomial Operators on the Brownian Bridge Measure

在L_p-范数逼近的意义下,本文确定了基于等距插值节点的Lagrange三角多项式插值列和Jackson三角多项式插值列在Brownian桥测度空间下的.p-平均误差的弱渐近阶.在信息基复杂性的意义下,由本文结果可知,如果可允许信息泛函为计算函数在固定点的值,那么当1≤p<∞时,基于等距插值节点的Lagrange三角多项式插值列和Jackson三角多项式插值列在Brownian桥测度空间下的p-平均误差弱等价于相应的最小非自适应p-平均信息半径.本文同时确定了最佳三角多项式逼近列, Fourier和逼近列,de la Vallee-Poussin和逼近列以及Jackson算子列在Brownian桥测度空间下的p-平均误差的弱渐近阶.

For the Lp-norm approximation, we determine the weakly asymptotically order for the p-average errors of Lagrange trigonometric interpolation polynomial sequence and Jackson trigonometric interpolation polynomial sequence based on the equidistant interpolation points on the Brownian bridge measure, In the sense of Information-based complexity, by our results we know that if permissible information functionals are function evaluations at fixed point, then the average errors of both Lagrange trigonometric interpolation polynomial sequence and Jackson trigonometric interpolation polynomial sequence based on the equidistant interpolation points are weakly equivalent to the corresponding sequence of minimal p-average radius of non- adaptive information for 1 ≤ p 〈 ∞. At the same time, we determine the weakly asymptotically order for the p-average errors of best trigonometric polynomial approximation, Fourier sums, de la Vallee-Poussin sums and Jackson integrals in the Brownian bridge measure.