J. Ledford

activity

20132026

most citedOn the Convergence of Regular Families of Cardinal Interpolators

18 citations · 55 across the 19 of their papers we have counts for

collaborators

22 papers

math.MG2026

The maximum volume polytope with nine vertices inscribed in the sphere

Steven Hoehner, Jeff Ledford

A classical problem in convex and discrete geometry asks for the convex polyhedron of greatest volume whose vertices are chosen from the unit sphere $S^{2}$ . For a prescribe…

math.FA2025

A note concerning fundamental functions of interpolation associated to the inverse multiquadric $(α^{2} + x^{2})^{- k}$

Jeff Ledford, Kyle Rutherford

This short note develops fundamental functions associated with the scattered shifts of the inverse \emph{multiquadric} function $(α^{2} + x^{2})^{- k}$ , for $k \in N$ .

math.MG2025

A note concerning frames and geometric inequalities

Jeff Ledford, Kevin Rivera-Ayala, Emma Schroeder

One may associate several frames to a given polytope, such as its collection of vertices, edges, or facet normal vectors. In this note, we use these frames to generate geometric in…

math.MG2024

Steiner symmetrization on the sphere

Bushra Basit, Steven Hoehner, Zsolt Lángi +1

The aim of this paper is to introduce a generalization of Steiner symmetrization in Euclidean space for spherical space, which is the dual of the Steiner symmetrization in hyperbol…

math.NA2023

A note concerning polyhyperbolic and related splines

Jeff Ledford, Luke Paris, Ryan Urban +1

This note concerns the interpolation problem with two parametrized families of splines related to polynomial spline interpolation. We address the questions of uniqueness and establ…

math.MG2022

Surface areas of equifacetal polytopes inscribed in the unit sphere $S^{2}$

Nicolas Freeman, Steven Hoehner, Jeff Ledford +2

This article is concerned with the problem of placing seven or eight points on the unit sphere $S^{2}$ in $R^{3}$ so that the surface area of the convex hull of the p…

math.MG2022

Extremal arrangements of points on the sphere for weighted cone-volume functionals

Steven Hoehner, Jeff Ledford

Weighted cone-volume functionals are introduced for the convex polytopes in $R^{n}$ . For these functionals, geometric inequalities are proved and the equality conditions are…

math.CA2021

A note concerning the invertibility of certain alternant matrices

Jeff Ledford

This brief note concerns the invertibility of certain alternant matrices. In particular those that consisting of polynomials and products of polynomials and logarithms are shown to…

math.CA2021

On non-local approximation properties of the binomial power functions $(1 + x^{q})^{r}$

Brock Erwin, Jeff Ledford, Kira Pierce

This note mainly concerns the binomial power function, defined as $(1 + x^{q})^{r}$ . We construct systems of polynomials related to non-local approximation, which allows us to establis…

math.FA2017

On the Structure and Interpolation Properties of Quasi Shift-invariant Spaces

Keaton Hamm, Jeff Ledford

The structure of certain types of quasi shift-invariant spaces, which take the form $V (ψ, X) := span^{L_{2}} {ψ (\cdot - x_{j}) : j \in Z}$ for a discrete s…

math.FA2016★ 8 cited

Regular Families of Kernels for Nonlinear Approximation

Keaton Hamm, Jeff Ledford

This article studies sufficient conditions on families of approximating kernels which provide $N$ --term approximation errors from an associated nonlinear approximation space which…

math.CA2015

Polyhyperbolic Cardinal Splines

Jeff Ledford

In this note we discuss solutions of differential equation $(D^{2} - α^{2})^{k} u = 0$ on $R ∖ Z$ , which we call hyperbolic splines. We develop the fundamental funct…

math.CA2015★ 8 cited

Cardinal Interpolation With General Multiquadrics: Convergence Rates

Keaton Hamm, Jeff Ledford

This article pertains to interpolation of Sobolev functions at shrinking lattices $h Z^{d}$ from $L_{p}$ shift-invariant spaces associated with cardinal functions related to ge…

math.CA2015

Recovering functions from the modulation spaces $F W$

Jeff Ledford

In this short note we show that functions in the modulation space $F W = {f : \sum_{j \in Z^{n}} ∥ f^(\cdot + 2 π j) ∥_{L_{\infty} ([- π, π]^{n})} < \infty}$ enjoy similar r…

math.CA2015★ 16 cited

Cardinal Interpolation With General Multiquadrics

Keaton Hamm, Jeff Ledford

This paper studies the cardinal interpolation operators associated with the general multiquadrics, $ϕ_{α, c} (x) = (∥ x ∥^{2} + c^{2})^{α}$ , $x \in R^{d}$ . These operators take the form…

math.FA2014

On regular families of cardinal interpolators and multiresolution analyses

Jeff Ledford

In this short note, we investigate the relationship between so-called regular families of cardinal interpolators and multiresolution analyses. We focus our studies on examples of r…

math.FA2014

Recovery of bivariate band limited functions using scattered translates of the Poisson kernel

Jeff Ledford

This paper continues the study of interpolation operators on scattered data. We introduce the Poisson interpolation operator and prove various properties. The main result concerns…

math.FA2013★ 4 cited

Convergence properties of spline-like cardinal interpolation operators acting on $l^{p}$ data

Jeff Ledford

If $f \in {f \in L^{p} (R) : f (x) = \int_{- π}^{π} e^{i x ξ} d β (ξ), β \in B . V . ([- π, π])}$ , then $f$ is determined by its samples on the integers by taking an appropriate limit. Specific…

math.FA2013★ 1 cited

Recovering functions from the Paley-Wiener amalgam space

Jeff Ledford

In this paper we show that functions from the Paley-Wiener amalgam space $(P W, l^{1}) = {f \in L^{2} (R) : \sum ∥ f^(ξ + 2 π m) ∥_{L^{2} ([- π, π])} < \infty}$ enjoy similar recovery…

math.FA2013★ 18 cited

On the Convergence of Regular Families of Cardinal Interpolators

Jeff Ledford

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 th…

math.FA2013

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

Jeff Ledford

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 multiqua…

math.FA2013

Approximating Continuous Functions with Scattered Translates of the Poisson Kernel

Jeff Ledford

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

The maximum volume polytope with nine vertices inscribed in the sphere

A note concerning fundamental functions of interpolation associated to the inverse multiquadric (α2+x2)−k

A note concerning frames and geometric inequalities

Steiner symmetrization on the sphere

A note concerning polyhyperbolic and related splines

Surface areas of equifacetal polytopes inscribed in the unit sphere S2

Extremal arrangements of points on the sphere for weighted cone-volume functionals

A note concerning the invertibility of certain alternant matrices

On non-local approximation properties of the binomial power functions (1+xq)r

On the Structure and Interpolation Properties of Quasi Shift-invariant Spaces

Regular Families of Kernels for Nonlinear Approximation

Polyhyperbolic Cardinal Splines

Cardinal Interpolation With General Multiquadrics: Convergence Rates

Recovering functions from the modulation spaces FW

Cardinal Interpolation With General Multiquadrics

On regular families of cardinal interpolators and multiresolution analyses

Recovery of bivariate band limited functions using scattered translates of the Poisson kernel

Convergence properties of spline-like cardinal interpolation operators acting on lp data

Recovering functions from the Paley-Wiener amalgam space

On the Convergence of Regular Families of Cardinal Interpolators

Non-local approximation of continuous functions using scattered translates of the general multiquadric (x2+c2)k−1/2

Approximating Continuous Functions with Scattered Translates of the Poisson Kernel

A note concerning fundamental functions of interpolation associated to the inverse multiquadric $(α^{2} + x^{2})^{- k}$

Surface areas of equifacetal polytopes inscribed in the unit sphere $S^{2}$

On non-local approximation properties of the binomial power functions $(1 + x^{q})^{r}$

Recovering functions from the modulation spaces $F W$

Convergence properties of spline-like cardinal interpolation operators acting on $l^{p}$ data

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