Multivariate sampling-type approximation
作者： A. Krivoshein , M. Skopina
DOI: 10.1142/S0219530516500147
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摘要: Approximation properties of the expansions ∑k∈ℤdLf(M−j⋅)(−k)φ(Mjx + k), where L is a linear differential operator and M matrix dilation, are studied. The sampling special case such expansions. Error estimations in Lp-norm, 2 ≤ p ≤∞, given terms Fourier transform f. approximation order depends on smoothness f, L, Strang–Fix condition for φ M. A wide class including both band-limited compactly supported functions considered, but compatibility with required. Such may be useful engineers.
sci-hub.se 参考文章(29)
Carl de Boor, Ronald A. DeVore, Amos Ron, Approximation from shift-invariant subspaces of ₂(^{}) Transactions of the American Mathematical Society. ,vol. 341, pp. 787- 806 ,(1994) , 10.1090/S0002-9947-1994-1195508-X
Bin Han, Zuowei Shen, Dual Wavelet Frames and Riesz Bases in Sobolev Spaces Constructive Approximation. ,vol. 29, pp. 369- 406 ,(2009) , 10.1007/S00365-008-9027-X
Rong-Qing Jia, Approximation properties of multivariate wavelets Mathematics of Computation. ,vol. 67, pp. 647- 665 ,(1998) , 10.1090/S0025-5718-98-00925-9
P.L. Butzer, J.R. Higgins, R.L. Stens, Classical and approximate sampling theorems: studies in the L P (R) and the uniform norm Journal of Approximation Theory. ,vol. 137, pp. 250- 263 ,(2005) , 10.1016/J.JAT.2005.07.011
C. Bardaro, P.L. Butzer, R.L. Stens, G. Vinti, Approximation error of the Whittaker cardinal series in terms of an averaged modulus of smoothness covering discontinuous signals Journal of Mathematical Analysis and Applications. ,vol. 316, pp. 269- 306 ,(2006) , 10.1016/J.JMAA.2005.04.042
Junjiang Lei, Rong-Qing Jia, E. W. Cheney, Approximation from Shift-Invariant Spaces by Integral Operators SIAM Journal on Mathematical Analysis. ,vol. 28, pp. 481- 498 ,(1997) , 10.1137/S0036141095279869
P. L. Butzer, R. L. Stens, Reconstruction of signals in L p (ℝ)-space by generalized sampling series based on linear combinations of B-splines† Integral Transforms and Special Functions. ,vol. 19, pp. 35- 58 ,(2008) , 10.1080/10652460701511285
Winfried Sickel, Spline Representations of Functions in Besov-Triebel-Lizorkin Spaces on ℝ n Forum Mathematicum. ,vol. 2, pp. 451- 476 ,(1990) , 10.1515/FORM.1990.2.451
P.L Butzer, S Ries, R.L Stens, Approximation of continuous and discontinuous functions by generalized sampling series Journal of Approximation Theory. ,vol. 50, pp. 25- 39 ,(1987) , 10.1016/0021-9045(87)90063-3
Winfried Sickel, Characterization of Besov-Triebel-Lizorkin spaces via approximation by Whittaker's cardinal series and related unconditional Schauder bases Constructive Approximation. ,vol. 8, pp. 257- 274 ,(1992) , 10.1007/BF01279019