|
|
具有特殊权重的Paley-Wiener空间上的线性宽度问题
|
Abstract:
带有限函数空间在数值分析、数据拟合等方面有广泛的应用，为许多问题提供了稳定性和可控性，能够有效地处理近似问题，找到最佳逼近方案。Paley-Wiener空间作为带有限函数空间的特殊情况，也是广泛应用于分析和信号处理等领域。本文研究加权多元Paley-Wiener空间在概率框架和平均框架下的逼近特征，特别地，利用离散化的方法估计了在概率框架和平均框架下，加权多元Paley-Wiener空间的线性n-宽度的精确渐进阶。
Spaces of bounded functions have wide applications in numerical analysis, data fitting, and other fields. They provide stability and controllability for many problems, effectively handling approximation problems and finding optimal approximation solutions. As a special case of spaces of bounded functions, Paley-Wiener spaces are also widely used in fields such as analysis and signal processing. This paper studies the approximation properties of weighted multivariate Paley-Wiener spaces in probability and average settings. Specifically, by using discretization methods, it estimates the exact asymptotic order of the linear n-width of weighted multivariate Paley-Wiener spaces in both the probabilistic and average settings.
| [1] | Packel, E.W. and Traub, J.F. (1987) Information-Based Complexity. Nature, 328, 29-33. https://doi.org/10.1038/328029a0 |
| [2] | Traub, J.F. and Wozniakowski, H. (1988) Infirmation Based Complexity. Academic Press. |
| [3] | Kolmogoroff, A. (1936) Uber Die Beste Annaherung Von Funktionen Einer Gegebenen Funktionenklasse. The Annals of Mathematics, 37, 107-110. https://doi.org/10.2307/1968691 |
| [4] | DeVore, R.A. and Lorentz, G.G. (1993) Constructive Approximation. Springer, 303. |
| [5] | Fang, G. and Chen, X. (2002) The Recovery of Functions of Paley-Wiener Class from Irregular Samplings. Acta Mathematica Scientia, 22, 466-472. https://doi.org/10.1016/s0252-9602(17)30319-3 |
| [6] | Fang, G.S. (2001) Recovery of Functions via Their Irregular Sampling Values. Science in China, 43, 268-271. |
| [7] | Ledford, J. (2013) Recovery of Paley-Wiener Functions Using Scattered Translates of Regular Interpolators. Journal of Approximation Theory, 173, 1-13. https://doi.org/10.1016/j.jat.2013.04.010 |
| [8] | Baxter, B.J.C. (1992) The Asymptotic Cardinal Function of the Multiquadratic (r) = (r2 + c2)1/2 as c → ∞. Computers & Mathematics with Applications, 24, 1-6. https://doi.org/10.1016/0898-1221(92)90166-f |
| [9] | Li, Y., Chen, G., Xu, Y. and Pan, X. (2024) The Approximation Characteristics of Weighted Band-Limited Function Space. Mathematics, 12, Article 1348. https://doi.org/10.3390/math12091348 |
| [10] | Bogachev, V. (1998) Gaussian Measures. American Mathematical Society. https://doi.org/10.1090/surv/062 |
| [11] | Maĭorov, V.E. (1994) Kolmogorov’s-Widths of Spaces of Smooth Functions. Russian Academy of Sciences. Sbornik Mathematics, 79, 265-279. https://doi.org/10.1070/sm1994v079n02abeh003499 |
