Approximation on the rotation group SO(3)
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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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ISRP Style
Zhuyuan Yang, Xin Wang, Xinzhi Liu, Approximation on the rotation group SO(3), Journal of Nonlinear Sciences and Applications, 10 (2017), no. 4, 1561--1568
AMA Style
Yang Zhuyuan, Wang Xin, Liu Xinzhi, Approximation on the rotation group SO(3). J. Nonlinear Sci. Appl. (2017); 10(4):1561--1568
Chicago/Turabian Style
Yang, Zhuyuan, Wang, Xin, Liu, Xinzhi. "Approximation on the rotation group SO(3)." Journal of Nonlinear Sciences and Applications, 10, no. 4 (2017): 1561--1568
Keywords
- Rotation group
- operator
- approximation.
MSC
References
-
[1]
D. I. Cartwright, K. Kucharski, Jackson’s theorem for compact connected Lie groups, J. Approx. Theory, 55 (1988), 352–359.
-
[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)
-
[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.
-
[5]
D. L. Ragozin, Approximation theory on SU(2), J. Approximation Theory, 1 (1968), 464–475.
-
[6]
D. Schmid, Marcinkiewicz-Zygmund inequalities and polynomial approximation from scattered data on SO(3), Numer. Funct. Anal. Optim., 29 (2008), 855–882.
-
[7]
M . R. Sepanski, Compact Lie groups, Springer-Verlag, Heidelberg (2007)
-
[8]
J. H. Xie, D. S. Fan, Asymptotic properties of Fourier coefficients on rotation groups, Kexue Tongbao (English Ed.), 32 (1987), 1590–1591.
-
[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.
-
[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.