Extension of Privaloff’s theorem to ultraspherical expansions

Calderón-zygmund Operators Associated to Ultraspherical Expansions

On Rapid Computation of Expansions in Ultraspherical Polynomials

We present an O(N log2 N) algorithm for the computation of the first N coefficients in the expansion of an analytic function in ultraspherical polynomials. We first represent expansion coefficients as an infinite linear combination of derivatives and then as an integral transform with a hypergeometric kernel along the boundary of a Bernstein ellipse. Following a transformation of the kernel, we...

An extension of Turán’s inequality for ultraspherical polynomials∗

Let pm(x) = P (λ) m (x)/P (λ) m (1) be the m-th ultraspherical polynomial normalized by pm(1) = 1. We prove the inequality |x|pn(x)−pn−1(x)pn+1(x) ≥ 0, x ∈ [−1, 1], for −1/2 < λ ≤ 1/2. Equality holds only for x = ±1 and, if n is even, for x = 0. Further partial results on an extension of this inequality to normalized Jacobi polynomials are given.

Berry-ess Een-type Inequalities for Ultraspherical Expansions

This paper contains several variants of Berry-Ess een-type inequalities for ultraspher-ical expansions of probability measures on 0; ]. Similar to the classical results on IR , proofs will be based in some cases on ultraspherical analogues of Fej er-kernels. The inequalities in this paper in particular lead to relations between the spherical-cap-distance of probability measures on unit spheres ...

An extension of the Wedderburn-Artin Theorem

‎In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.