An Uncertainty Principle for Ultraspherical Expansions

Calderón-zygmund Operators Associated to Ultraspherical Expansions

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 ...

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 uncertainty principle for quaternion Fourier transform

We review the quaternionic Fourier transform (QFT). Using the properties of the QFT we establish an uncertainty principle for the right-sided QFT. This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains. It is shown that only a Gaussian quaternion signal minimizes the uncertainty.

An Uncertainty Principle for Function Fields

In a recent work [8], Granville and Soundararajan established a so-called “uncertainty principle” for arithmetic sequences. Loosely speaking, this means that sequences of integers which are determined by arithmetic constraints cannot always be well-distributed. In particular, suppose that A is a sequence of integers and S is an integer, such that for all d with (d,S) = 1, the proportion of elem...