Approximation of functions on the Sobolev space with a Gaussian measure

作者：Wang HePing^*; Zhang YanWei; Zhai XueBo

来源：Science China Mathematics, 2010, 53(2): 373-384.

DOI：10.1007/s11425-009-0113-8

• average width
• best approximation
• approximation by linear operators
• Sobolev space
• Gaussian measure

We discuss the best approximation of periodic functions by trigonometric polynomials and the approximation by Fourier partial summation operators, Vallee-Poussin operators, Cesaro operators, Abel operators, and Jackson operators, respectively, on the Sobolev space with a Gaussian measure and obtain the average error estimations. We show that, in the average case setting, the trigonometric polynomial subspaces are the asymptotically optimal subspaces in the L-q space for 1 <= q < infinity, and the Fourier partial summation operators and the Vallee-Poussin operators are the asymptotically optimal linear operators and are as good as optimal nonlinear operators in the L-q space for 1 <= q < infinity.

• 出版日期2010-2
• 单位首都师范大学; 枣庄学院