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Nonlinear Approximation by Trigonometric Sums

Authors:	RA DeVore VN Temlyakov

Institution:	(1) Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208, USA

Abstract:	We investigate the -error of approximation to a function $f\in L_p({\Bbb T}^d)$ by a linear combination $\sum_{k}c_ke_k$ of exponentials $e_k(x):= e^{i\langle k,x\rangle}=e^{i(k_1x_1+\cdots+k_dx_d)}$ on ${\Bbb T}^d,$ where the frequencies $k\in {\Bbb Z}^d$ are allowed to depend on We bound this error in terms of the smoothness and other properties of and show that our bounds are best possible in the sense of approximation of certain classes of functions.

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