Jin Chen^*, Wenjing Lu, Hanyue Xiao, Yanan Wang, Xin Tan

Show more
School of Science, Xihua University, Chengdu, China.
Show less

Keywords: Entropy Number, The Finite Dimensional Diagonal Operator, The Infi nite Dimensional Diagonal Operator

Cite this paper: Chen, J. , Lu, W. , Xiao, H. , Wang, Y. and Tan, X. (2019) Entropy Number of Diagonal Operator. Journal of Applied Mathematics and Physics, 7, 738-745. doi: 10.4236/jamp.2019.73051.

References

[1]   Pietsch, A. (1978) Operator Ideals. In: Mathematische Monographien, Vol. 16, VEB, Deutscher Verlag der Wissenschaften,Berlin. (Reprinted in North-Holland, Amsterdam-New York,1980, 168-175)

[2]   Schutt, C. (1984) Entropy Numbers of Diagonal Operators between Symmetric Banach Spaces. Journal of Approximation Theory, 40, 121-128.
https://doi.org/10.1016/0021-9045(84)90021-2

[3]   Kuhn, T. (2005) Entropy Numbers of General Diagonal Operators. Revista Matemtica Complutense, 18, 479-491.

[4]   Carl, B. and Stephani, I. (1990) Entropy, Compactness and the Approximation of Operators. In: Bollabas, B., Fulton, W., Kirwan, F., Sarnak, P., Simon, B. and Totaro, B., Eds., Cambridge Tracts in Mathematics, Vol. 98, Cambridge University Press,Cambridge.
https://doi.org/10.1017/CBO9780511897467

[5]   Belinsky, E.S. (1998) Estimates of Entropy Numbers and Gaussian Measures for Classes of Functions with Bounded Mixed Derivative. Journal of Approximation Theory, 93, 114-127.
https://doi.org/10.1006/jath.1997.3157

[6]   Dung, D. (2001) Non-Linear Approximations Using Sets of Finite Cardinality or Finite Pseudo-Dimension. Constructive Approximation, 17, 467-492.

[7]   Lorentz, G.G., Golitschek, M.V. and Makovoz, Y. (1985) Constructive Approximation. Springer, Berlin.

[8]   Carl, B. (1981) Entropy Numbers, s-Numbers, and Eigenvalue Problems. Journal of Functional Analysis, 41, 290-306.
https://doi.org/10.1016/0022-1236(81)90076-8

[9]   Carl, B. (1981) Entropy Numbers of Embedding Maps between Besov Spaces with an Application to Eigenvalue Problems. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 90, 63-70.

[10]   Edmunds, D.E. and Triebel, H. (1996) Function Spaces, Entropy Numbers, Di erential Operators. In: Bollabas, B., Fulton, W., Kirwan, F., Sarnak, P., Simon, B. and Totaro, B., Eds., Cambridge Tracts in Mathematics, Vol. 120, Cambridge University Press, Cambridge.
https://doi.org/10.1017/CBO9780511662201

[11]   Haroske, D.D. and Triebel, H. (2005) Wavelet Bases and Entropy Numbers in Weighted Function Spaces. Mathematische Nachrichten, 278, 108-132.
https://doi.org/10.1002/mana.200410229