arXiv subjects

Jeff Ledford

Publications and source records attributed to Jeff Ledford.

23 records · Page 2Linked to original sources

arXiv2013

Recovering functions from the Paley-Wiener amalgam space

In this paper we show that functions from the Paley-Wiener amalgam space $(PW,l^1)=\{f\in L^2(\mathbb{R}): \sum\|\hat{f}(ξ+2πm) \|_{L^2([-π,π])} < \infty\}$ enjoy similar recovery properties as the classical Paley-Wiener space. Specifically, if $\{ϕ_α(x): α\in A\}$ is a regular family of interpolators and $\{x_n: n\in \mathbb{Z}\}$ is a complete interpolating sequence for $L^2([-π,π])$, then the family $\{ e^{2πi m x}ϕ_α(x-x_n): m,n\in \mathbb{Z}, α\in A \} $ may be used to recover $f\in(PW,l^1)$.

math.FA↗

arXiv2013

On the Convergence of Regular Families of Cardinal Interpolators

In this note a general way to develop a cardinal interpolant for $l^2$-data on the integer lattice $Z^n$ is shown. Further, a parameter is introduced which allows one to recover the original Paley-Weiner function from which the data came.

math.FA↗

arXiv2013

Non-local approximation of continuous functions using scattered translates of the general multiquadric $(x^2+c^2)^{k-1/2}$

This article shows that on a closed interval $[a,b]$ a continuous function may be approximated to an arbitrary degree of accuracy using scattered translates of the general multiquadric $(x^2+c^2)^{k-1/2}$.

math.FA↗

arXiv2013

Recovery of Paley-Wiener functions using scattered translates of regular interpolators

It has been shown that Paley-Wiener functions may be recovered from their values on a complete interpolating sequence. This paper explores the same phenomenon, and gives a sufficient condition on a function $ϕ(x)$, called an interpolator, so that scattered translates of this function may be used to interpolate and recover any given Paley-Wiener function.

math.FA↗

arXiv2013

Approximating Continuous Functions with Scattered Translates of the Poisson Kernel

The goal of this note is to show that continuous functions may be approximated using scattered translates of the Poisson kernel.

math.FA↗