Polynomials with positive coefficients: Uniqueness of best approximation

Approximation by Polynomials with Coefficients

Roots of polynomials with positive coefficients

We describe the limit zero distributions of sequences of polynomials with positive coefficients. We also characterize the polynomials with real coefficients for which some power has positive coefficients. MSC Primary: 30C15, 26C10, secondary: 31A05.

On the Uniqueness of Best L2[0,1] Approximation by Piecewise Polynomials With Variable Breakpoints*

In this paper a sufficient condition for the uniqueness of best L2[0,1] approximation by piecewise polynomials of order k with variable breakpoints is generalized from that of order 2. Other extensions included here are nonuniqueness and eventual uniqueness results.

Approximation by Polynomials with Nonnegative Coefficients and the Spectral Theory of Positive Operators

For Σ a compact subset of C symmetric with respect to conjugation and f : Σ → C a continuous function, we obtain sharp conditions on f and Σ that insure that f can be approximated uniformly on Σ by polynomials with nonnegative coefficients. For X a real Banach space, K ⊆ X a closed but not necessarily normal cone with K −K = X, and A : X → X a bounded linear operator with A[K] ⊆ K, we use these...

An Inequality for Polynomials with Positive Coefficients and Applications in Rational Approximation

We extend an inequality of Leviatan and Lubinsky ([3: Theorem 3.1]) to polynomials with positive coefficients. Two applications in approximation by rational functions with prescribed numerators are given.