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1.
S. P. Voitenko 《Ukrainian Mathematical Journal》2009,61(9):1404-1416
We obtain exact order estimates for the best M -term trigonometric approximations of the classes Bp,qW B_{p,\theta }^\Omega of periodic functions of many variables in the space L
q
. 相似文献
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K. V. Solich 《Ukrainian Mathematical Journal》2011,63(6):940-961
We obtain exact-order estimates for the best bilinear approximations of the classes Sp,qW B S_{p,\theta }^\Omega B of periodic functions of many variables in the space L
q
under certain restrictions on the parameters p, q, and θ. 相似文献
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A. S. Romanyuk 《Ukrainian Mathematical Journal》1992,44(5):596-606
We study classes of periodic functions of several variables with bounded generalized derivative in the metric of the space Lp. We obtain order estimates of deviations of Fourier sums, which are constructed depending on the behavior of functions that define the operator of generalized differentiation. We find estimates of the Kolmogorov widths, which are realized by the Fourier sums that are constructed.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 5, pp. 662–672, May, 1992. 相似文献
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É. M. Galeev 《Mathematical Notes》1990,47(3):248-254
Translated from Matematicheskii Zametki, Vol. 47, No. 3, pp. 32–41, March, 1990. 相似文献
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We obtain order estimates for the approximation of the classes
of periodic functions of many variables in the space L
q by using operators of orthogonal projection and linear operators satisfying certain conditions. 相似文献
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Din' Zung 《Journal of Mathematical Sciences》1986,35(6):2859-2875
The paper deals with imbedding theorems and harmonic approximation for classes of periodic functions of several variables. Necessary and sufficient conditions for imbedding are found for various classes of smooth functions. The paper contains asymptotic estimates for fractional order derivatives of multidimensional Dirichlet and Favard kernels, for Fourier best approximation and for the Kolmogorov diameter of smooth function classes.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 10, pp. 207–226, 1984. 相似文献
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A. S. Romanyuk 《Ukrainian Mathematical Journal》1991,43(10):1297-1306
Order estimates are obtained for best approximations by polynomials constructed according to hyperbolic crosses on the classes B
p
r
, of periodic functions of several variables. The order is found of the Kolmogorov width on these classes in the spaces Lq for 1 <p q 2.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 10, pp. 1398–1408, October, 1991. 相似文献
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R. V. Tovkach 《Ukrainian Mathematical Journal》2011,62(8):1339-1343
We obtain the exact order of deviations of Fejér sums on the class of continuous functions. This order is determined by a
given majorant of the best approximations. 相似文献
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We obtain exact order estimates for the approximation of the classes B
p,θ
Ω
of periodic functions of many variables in the space L
q
by using operators of orthogonal projection and linear operators satisfying certain conditions.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 5, pp. 692–704, May, 2006. 相似文献
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We obtain order estimates for the best M-term trigonometric approximations of the classes $ B^{Omega }_{{p,{text{ $ B^{Omega }_{{p,{text{ of periodic functions of many variables in the space L q for several values of the parameters p and q. 相似文献