3 citations · 9 across the 11 of their papers we have counts for
13 papers
Sketching the Heat Kernel: Using Gaussian Processes to Embed Data
Anna C. Gilbert, Kevin O'Neill
This paper introduces a novel, non-deterministic method for embedding data in low-dimensional Euclidean space based on computing realizations of a Gaussian process depending on the…
A Whitney Extension Problem for Manifolds
Kevin O'Neill
The purpose of this paper is to address a manifold-based version of Whitney's extension problem: Given a compact set , how can we tell if there exists a -d…
On Solutions to Systems of Linear Inequalities
Garving K. Luli, Kevin O'Neill
Recent work of C. Fefferman and the first author has demonstrated that the linear system of equations \begin{equation*} \sum_{j=1}^M A_{ij}(x)F_j(x)=f_i(x)\hspace{.2in} (i=1,...,N)…
Smooth Selection for Infinite Sets
Fushuai Jiang, Garving K. Luli, Kevin O'Neill
Whitney's extension problem asks the following: Given a compact set and a function , how can we tell whether there exists $F\in C^m(\mathb…
On the Shape Fields Finiteness Principle
Fushuai Jiang, Garving K. Luli, Kevin O'Neill
In this paper, we improve the finiteness constant for the finiteness principles for and selection proven by…
A Quantitative Stability Theorem for Convolution on the Heisenberg Group
Kevin O'Neill
Although convolution on Euclidean space and the Heisenberg group satisfy the same bounds with the same optimal constants, the former has maximizers while the latter does not.…
Oscillatory Loomis-Whitney and Projections of Sublevel Sets
Maxim Gilula, Kevin O'Neill, Lechao Xiao
We consider an oscillatory integral operator with Loomis-Whitney multilinear form. The phase is real analytic in a neighborhood of the origin in and satisfies a nond…
Decay Rate of n-Linear Oscillatory Integral Operators in
Aleksandra Niepla, Kevin O'Neill, Zhen Zeng
In this paper, we prove decay estimates for multilinear oscillatory integrals in , establishing sharpness through a scaling argument. The result in this paper i…
Estimating Oscillatory Integrals of Convolution Type in
Aleksandra Niepla, Kevin O'Neill, Zhen Zeng
In this paper, we prove an decay estimate for a trilinear oscillatory integral of convolution type in which recovers the earlier result of Li (2013) w…
A Sharpened Inequality for Twisted Convolution
Kevin O'Neill
Consider the trilinear form for twisted convolution on : \begin{equation*} \mathcal{T}_t(\mathbf{f}):=\iint f_1(x)f_2(y)f_3(x+y)e^{itσ(x,y)}dxdy,\end{equation*} wh…
A Sharpened Rearrangement Inequality for Convolution on the Sphere
Kevin O'Neill
One may define a trilinear convolution form on the sphere involving two functions on the sphere and a monotonic function on the interval . A symmetrization inequality of Ba…
Maximizers of Rogers-Brascamp-Lieb-Luttinger functionals in higher dimensions
Michael Christ, Kevin O'Neill
A symmetrization inequality of Rogers and of Brascamp-Lieb-Luttinger states that for a certain class of multilinear integral expressions, among tuples of sets of prescribed Lebesgu…
A Variation on Hölder-Brascamp-Lieb Inequalities
Kevin O'Neill
The Hölder-Brascamp-Lieb inequalities are a collection of multilinear inequalities generalizing a convolution inequality of Young and the Loomis-Whitney inequalities. The full rang…