In this paper, we continue studying the so-called non-linear best m-term one-sided approximation problems and obtain the asymptotic estimations of non-linear best m-term one-sided trigonometric approximation under the norm L p (1 ≤ p ≤ ∞) of multiplier function classes and the corresponding m-term Greedy-liked one-sided trigonometric approximation results. [ABSTRACT FROM AUTHOR]
We construct majorants and minorants of a Gaussian function in Euclidean space that have Fourier transforms supported in a box. The majorants that we construct are shown to be extremal and our minorants are shown to be asymptotically extremal as the sides of the box become uniformly large. We then adapt the Distribution and Gaussian Subordination methods of [12] to the multidimensional setting to obtain majorants and minorants for a class of radial functions. Periodic analogues of the main results are proven and applications to Hilbert-type inequalities are given. [ABSTRACT FROM AUTHOR]
We present some operators for one-sided approximation of Riemann integrable functions on [0, 1] by algebraic polynomials in Lp-spaces. The estimates for the error of approximation are given with an explicit constant. [ABSTRACT FROM AUTHOR]