Approximation on the rotation group SO(3)

Volume 10, Issue 4, pp 1561--1568 http://dx.doi.org/10.22436/jnsa.010.04.22

Publication Date: April 20, 2017 Submission Date: July 11, 2016

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Authors

Zhuyuan Yang - School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, P. R. China. Xin Wang - School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, P. R. China. Xinzhi Liu - Department of Mathematics, University of Waterloo, Waterloo, Canada N2L 3G1.

Abstract

In this paper we study the approximation on rotation group SO(3), we consider the partial sum, Fejér and Jackson-type operators and obtain the approximation theorems in \(L_p(1 \leq p \leq\infty)\) respectively

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Keywords

• Rotation group
• operator
• approximation.

MSC

•  41A25
•  41A35
•  41A60

References

• [1] D. I. Cartwright, K. Kucharski, Jackson’s theorem for compact connected Lie groups, J. Approx. Theory, 55 (1988), 352–359.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] S. Gong, Dianxing qun shangde tiaohe fenxi, (Chinese) [[Harmonic analysis on classical groups]] Chuncui Shuxue yu Yingyong Shuxue Zhuanzhu [Series of Monographs in Pure and Applied Mathematics], Kexue Chubanshe (Science Press), Beijing (1983)
  • MathSciNet


• [3] Q.-Z. Han, H.-Z. Sun, Group theory, Peking University Press, Beijing (1987)


• [4] R. Hielscher, J. Prestin, A. Vollrath, Fast summation of functions on the rotation group, Math. Geosci., 42 (2010), 773–794.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] D. L. Ragozin, Approximation theory on SU(2), J. Approximation Theory, 1 (1968), 464–475.
  • MathSciNet


• [6] D. Schmid, Marcinkiewicz-Zygmund inequalities and polynomial approximation from scattered data on SO(3), Numer. Funct. Anal. Optim., 29 (2008), 855–882.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] M . R. Sepanski, Compact Lie groups, Springer-Verlag, Heidelberg (2007)
  • Google Scholar


• [8] J. H. Xie, D. S. Fan, Asymptotic properties of Fourier coefficients on rotation groups, Kexue Tongbao (English Ed.), 32 (1987), 1590–1591.
  • MathSciNet
  • Google Scholar
  • MATH


• [9] W. T. Xu, X. L. Ka, Group theory and its applications in solid state physics, (Chinese), Higher Education Press, Beijing (1999)


• [10] X. A. Zheng, Harmonic analysis on compact homogeneous spaces, Shanghai Scientific and Technical Publishers, Chinese (1999)


• [11] X. A. Zheng, Z. F. Xu, H. S. Zhao, Approximation by polynomials on compact Lie groups, I, Best uniform approximation to continuous functions , (Chinese) Adv. in Math. (Beijing), 16 (1987), 61–66.
  • MathSciNet


• [12] X. A. Zheng, H. S. Zhao, Z. F. Xu, Approximation by polynomials on compact Lie groups, II, Best approximation in the \(L_p\) norm, (Chinese) Adv. in Math. (China), 19 (1990), 199–203.
  • MathSciNet