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球面Jackson多项式逼近 被引量:2

APPROXIMATION BY SPHERICAL JACKSON POLYNOMIALS
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摘要 讨论了球面Jackson多项式逼近的若干性质。应用K-泛函和乘子方法建立了球面Jackson多项式逼近的正定理、逆定理和饱和定理。 Approximation properties of Jackson polynomials defined on the unit sphere of the Euclidean space R~# are studied. Using methods of K-functional and multiplier the direct, inverse and saturation theorems are established.
出处 《北京师范大学学报(自然科学版)》 CAS CSCD 1991年第1期6-12,共7页 Journal of Beijing Normal University(Natural Science)
基金 国家自然科学基金
关键词 球面 J-多项式 逼近 饱和阶 饱和类 spherical Jackson polynomial approximation saturation order saturation class..,.
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参考文献2

  • 1Erich Wickeren. Steckin-marchaud-type inequalities in connection with bernstein polynomials[J] 1986,Constructive Approximation(1):331~337
  • 2П. И. ЛИЗОРКИН,С. М. никольский. A theorem concerning approximation on the sphere[J] 1983,Analysis Mathematica(3):207~221

同被引文献13

  • 1Ditzian Z. Jackson-type inequality on the sphere [J]. Acta Math Hungar, 2004, 102(1 2):1-35.
  • 2Riemenschneider S, Wang K Y. Approximation theorems of Jackson type on the sphere [J]. Adv in Math (China), 1995, 24(2):184-186.
  • 3Dai F, Ditzian Z. Jackson theorem in Lp, 0 < p < 1, for functions on the sphere [J]. J Approx Theory, 2010, 162(2):382-391.
  • 4Lizorkin P I, Nikol'skii S M. A theorem concerning approximation on the sphere [J]. Anal Math, 1983, 9:20-221.
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  • 6Ditzian Z, Runovskii K. Averages on caps of S^d-1 [J]. J Math Anal Appl, 2000, 248:260- 274.
  • 7Belinsky E, Dai F, Ditzian Z. Multivariate approximating averages [J]. Y Approx Theory, 2003, 125:85-105.
  • 8Wang K Y, Li L Q. Harmonic analysis and approximation on the unit sphere [M]. Beijing: Science Press, 2000.
  • 9Freeden W, Gervens T, Schreiner M. Constructive approximation on the sphere [M]. New York: Oxford University Press Ine, 1998.
  • 10Miiller C. Spherical harmonics [M]//Lecture Notes in Mathematics. Vol 17, Berlin: Springer-Verlag, 1966.

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