无穷维恒等算子的伪宽度

Pseudo n-Width of Infinite Dimension Identity Operator

摘要: 本文讨论了无穷维恒等算子的伪宽度，并计算了其精确渐近阶。

Abstract: In this paper, we study the pseudo width of infinite dimension identity operator , and obtain its asymptotic degree.

文章引用：陆文静, 肖寒月, 秦静. 无穷维恒等算子的伪宽度[J]. 应用数学进展, 2019, 8(4): 747-752. https://doi.org/10.12677/AAM.2019.84084

参考文献

[1]	Traub, J.F. Wasilkowski, G.W. and Wozniakowski, H. (1988) Information-Based Complexity. Academic Press, Bos-ton.
[2]	Vapnik, V.N. and Chervonenkis, A.Ya. (1971) On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities. Theory of Probability & Its Applications, 16, 264-280. [Google Scholar] [CrossRef]
[3]	Vapnik, V.N. and Cbervonenkis, A.Ya. (1981) Necessary and Sufficient Conditions for the Uniform Convergence of Means to Their Expectations. Theory of Probability & Its Applications, 26, 532-553. [Google Scholar] [CrossRef]
[4]	Pollard, D. (1989) Empiricai Processes: Theory and Applications. NSF-CBMS Regional Conference Sews in Probability and Statistics, Vol. 2, Institute of Mathmatical Statistics and American Statistical Association.
[5]	Haussler, D. (1992) Decision Theoretic Generalizations of the PAC Model for Neural Net and Other Learning Applications. Information and Computation, 100, 78-150. [Google Scholar] [CrossRef]
[6]	Vapnik, V.N. (1982) Estimation of Dependences Based on Empirical Data. Springer. Berlin.
[7]	Maiorova, V. and Ratsaby, J. (1998) The Degree of Approximation of Sets in Euclidean Space Using Sets with Bounded Vapnik-Chervonenkis Dimension. Discrete Applied Mathematics, 86, 81-93. [Google Scholar] [CrossRef]
[8]	Chen, G.G., Fang, G.S. and Ruan, Y.L. (2007) Non-Linear Approximation of Functions with Mixed Smoothness by Sets of Finite Pseudo-Dimension. Acta Mathematica Sinica, English Series, 23, 671-676. [Google Scholar] [CrossRef]