Degree of uniform approximation on disjoint intervals

On Constrained Uniform Approximation

Non-uniform spline recovery from small degree polynomial approximation

We investigate the sparse spikes deconvolution problem onto spaces of algebraic polynomials. Our framework encompasses the measure reconstruction problem from a combination of noiseless and noisy moment measurements. We study a TV-norm regularization procedure to localize the support and estimate the weights of a target discrete measure in this frame. Furthermore, we derive quantitative bounds ...

Polynomials of the best uniform approximation to sgn(x) on two intervals

We describe polynomials of the best uniform approximation to sgn(x) on the union of two intervals [−A,−1] ∪ [1, B] in terms of special conformal mappings. This permits us to find the exact asymptotic behavior of the error of this approximation. MSC 41A10, 41A25, 30C20.

Solving Inverse Sturm-Liouville Problems with Transmission Conditions on Two Disjoint Intervals

‎In the present paper‎, ‎some spectral properties of boundary value problems of Sturm-Liouville type on two disjoint bounded intervals with transmission boundary conditions are investigated‎. ‎Uniqueness theorems for the solution of the inverse problem are proved‎, ‎then we study the reconstructing of the coefficients of the Sturm-Liouville problem by the spectrtal mappings method.

On uniform approximation by splines

for 0 ≤ r ≤ k − 1. In particular, dist (f, S π) = O(|π| ) for f ∈ C(I), or, more generally, for f ∈ C(I), such, that f (k−1) satisfies a Lipschitz condition, a result proved earlier by different means [2]. These results are shown to be true even if I is permitted to become infinite and some of the knots are permitted to coalesce. The argument is based on a “local” interpolation scheme Pπ by spl...