Acta mathematica scientia, Series B >
THE SHARP JACKSON INEQUALITY FOR L2-APPROXIMATION ON THE PERIODIC CYLINDER
Received date: 2014-04-02
Revised date: 2014-07-01
Online published: 2015-03-20
Supported by
This research was supported by National Natural Science Foundation of China (11071019), and Beijing Natural Science Foundation (1132001).
We consider Jackson inequality in L2(Bd×T,Wκ,μB (x)), where the weight function Wκ,μB (x)) is defined on the ball Bd and related to reflection group, and obtain the sharp Jackson inequality
En-1,m-1(f)2≤Kn,m(τ, r)ωr(f, t)2,τ≥2τn,λ,
where τn,λ is the first positive zero of the Gegenbauer cosine polynomial Cnλ(cosθ)(n∈N).d:\PDF\10.16381/j.cnki.issn1003-207x.2015.04.020.pdf
Yi GU , Yongping LIU . THE SHARP JACKSON INEQUALITY FOR L2-APPROXIMATION ON THE PERIODIC CYLINDER[J]. Acta mathematica scientia, Series B, 2015 , 35(2) : 375 -382 . DOI: 10.1016/S0252-9602(15)60009-1
[1] Chernykh N I. Jackson's inequality in L2. Trudy Mat Inst Steklov, 1967, 88: 71-74
[2] Chernykh N I. The best approximation of periodic functions by trigonometric polynomials in L2. Mat Zametki, 1967, 2: 513-522
[3] Arestov V V, Chernykh N I. On the L2-approximation of periodic functions by trigonometric polynomials. Approximation and function spaces. Gdańsk, 1979. Amsterdam: North-Holland, 1981: 25-43
[4] Kozko A I, Rozhdestvenskii A V. On Jackson's inequality with a generalized modulus of continuity. Mat Zametki, 2003, 73(5): 783-788
[5] Vasil'ev S N. Exact Jackson-stechkin type inequality in L2 for the best approximations by trigonometric polynomials. Electronic J Investigated in Russia, 2002, 140: 1577-1586
[6] Arestov V V, Babenko A G. On the optimal point in Jackson's inequality in L2(-∞,∞) with the second modulus of continuity. East J Approx, 2004, 10(1/2): 201-214
[7] Yudin V A. A multidimensional Jackson theorem. Mat Zametki, 1976, 20(3): 439-444; Presented at the International Conference on the Theory of Approximation of Functions, held at Kaluga, July 24-28, 1975
[8] Arestov V V, Popov V Yu. Jackson inequalities on a sphere in L2. Izv Vyssh Uchebn Zaved Mat, 1995, (8): 13-20
[9] Babenko A G. Exact Jackson-Stechkin inequality in the space L2 of functions on a multidimensional sphere. Mat Zametki, 1996, 60(3): 333-355
[10] Sun Huan. The sharp Jackson inequalities for L2-approximation on the disk and the real line with weight
[Master's thesis]. Beijing Normal University, 2012
[11] Gu Yi, Liu Yongping. The sharp constants in the Jackson inequality in weighted L2(Bd). Journal of Beijing Normal University (Nature Science) (in Chinese), 2013, 49(4): 347-350
[12] Xu Yuan. Generalized translation operator and approximation in several variables. J Comput Appl Math, 2005, 178(1/2): 489-512
/
| 〈 |
|
〉 |