Garving K. Luli

activity

20122026

C^{2} (R^{2})

Interpolation

8 citations · 19 across the 16 of their papers we have counts for

collaborators

22 papers

math.CA2026

Semialgebraic $C^{m}$ solutions to a univariate system of linear inequalities with Nash forcing

Fushuai Jiang, Garving K. Luli

Let $(A_{ij} (x))_{1 \leq i \leq N, 1 \leq j \leq M}$ be a matrix of univariate semialgebraic functions. We study the solvability of the system of linear inequalities \begin{equatio…

math.CA2026

Smooth solutions to systems of linear inequalities on $R$

Fushuai Jiang, Garving K. Luli

Fix an integer $m \geq 0$ . We study the one-dimensional problem of deciding when a system of linear inequalities \begin{equation*} \sum_{j=1}^M A_{ij}(x)F_j(x)\leq f_i(x),\qquad i=1…

math.CA2026

Optimal $C^{1, 1}$ and Quasi-Optimal $C^{2}$ Monotone Interpolation with Curvature Control

Fushuai Jiang, Garving K. Luli

We study monotone Hermite interpolation on an interval, where both function values and first derivatives are prescribed at the nodes. Among all $C^{1, 1}$ interpolants, we seek one…

math.CA2023

On $C^{m}$ 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)…

math.FA2021

Smooth Selection for Infinite Sets

Fushuai Jiang, Garving K. Luli, Kevin O'Neill

Whitney's extension problem asks the following: Given a compact set $E \subset R^{n}$ and a function $f : E \to R$ , how can we tell whether there exists $F\in C^m(\mathb…

math.CA2021

$C^{2}$ Interpolation with Range Restriction

Charles Fefferman, Fushuai Jiang, Garving K. Luli

Given $- \infty < λ < Λ < \infty$ , $E \subset R^{n}$ finite, and $f : E \to [λ, Λ]$ , how can we extend $f$ to a $C^{m} (R^{n})$ function $F$ such that $ λ\leq F \…

math.CA2021★ 8 cited

Algorithms for Nonnegative $C^{2} (R^{2})$ Interpolation

Fushuai Jiang, Garving K. Luli

Let $E \subset R^{2}$ be a finite set, and let $f : E \to [0, \infty)$ . In this paper, we address the algorithmic aspects of nonnegative $C^{2}$ interpolation in the plane.…

math.CA2021

$C^{m}$ Semialgebraic Sections Over the Plane

Charles L. Fefferman, Garving K. Luli

In this paper we settle the two-dimensional case of a conjecture involving unknown semialgebraic functions with specified smoothness. More precisely, we prove the following result:…

math.FA2020★ 1 cited

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 $C^{m} (R^{n}, R^{d})$ and $C^{m - 1, 1} (R^{n}, R^{D})$ selection proven by…

math.CA2020

$C^{2} (R^{2})$ Nonnegative Extension by Bounded-depth Operators

Fushuai Jiang, Garving K. Luli

In this paper, we prove the existence of a nonnegative parameter-dependent (nonlinear) $C^{2} (R^{2})$ extension operator with bounded depth.

math.CA2019

Solutions to a System of Equations for $C^{m}$ Functions

Charles Fefferman, Garving K. Luli

Fix $m \geq 0$ , and let $A = (A_{ij} (x))_{1 \leq i \leq N, 1 \leq j \leq M}$ be a matrix of semialgebraic functions on $R^{n}$ or on a compact subset $E…

math.CA2019

Generators for the $C^{m}$ -closures of Ideals

Charles Fefferman, Garving K. Luli

Let $R$ denote the ring of real polynomials on $R^{n}$ . Fix $m \geq 0$ , and let $A_{1}, \dots, A_{M} \in R$ . The $C^{m}$ -closure of $\left( A_{1},\cdots…

math.CA2019

Nonnegative $C^{2} (R^{2})$ interpolation

Fushuai Jiang, Garving K. Luli

In this paper, we prove two improved versions of the Finiteness Principle for nonnegative $C^{2} (R^{2})$ interpolation, previously proven by Fefferman, Israel, and Luli. The…

math.AP2017★ 3 cited

On one-dimension semi-linear wave equations with null conditions

Garving K. Luli, Shiwu Yang, Pin Yu

It is well-known that in dimensions at least three semilinear wave equations with null conditions admit global solutions for small initial data. It is also known that in dimension…

math.CA2016

Interpolation of data by smooth non-negative functions

Charles Fefferman, Arie Israel, Garving K. Luli

We prove a finiteness principle for interpolation of data by nonnegative Cm functions. Our result raises the hope that one can start to understand constrained interpolation problem…

math.FA2016★ 1 cited

Finitness Principles for Smooth Selection

Charles Fefferman, Arie Israel, Garving K. Luli

In this paper we prove finiteness principles for $C^{m} (R^{n}, R^{D})$ -selection, and for $C^{m - 1, 1} (R^{n}, R^{D})$ -se…

math.CA2015

Finiteness Principles for Smooth Selection

Charles Fefferman, Arie Israel, Garving K. Luli

In this paper we prove finiteness principles for $C^{m} (R^{n}, R^{D})$ -selection, and for $C^{m - 1, 1} (R^{n}, R^{D})$ -se…

math.AP2015★ 2 cited

On the generalized Buckley-Leverett equation

Jan Burczak, Rafael Granero-Belinchón, Garving K. Luli

In this paper we study the generalized Buckley-Leverett equation with nonlocal regularizing terms. One of these regularizing terms is diffusive, while the other one is conservative…

math.CA2014★ 1 cited

Fitting a Sobolev function to data

Charles L. Fefferman, Arie Israel, Garving K. Luli

We exhibit an algorithm to solve the following extension problem: Given a finite set $E \subset R^{n}$ and a function $f : E \to R$ , compute an extension $F$ …

math.AG2012

The Brenner-Hochster-Kollár and Whitney Problems for Vector-valued Functions and Jets

Charles L. Fefferman, Garving K. Luli

In this paper, we give analytic methods for finding m (and m+ω) times continuously differentiable solutions of a finite system of linear equations. Along the way, we also solve a g…

math.CA2012

The Structure of Sobolev Extension Operators

Charles L. Fefferman, Arie Israel, Garving K. Luli

Let $L^{m, p} (R^{n})$ denote the Sobolev space of functions whose $m$ -th derivatives lie in $L^{p} (R^{n})$ , and assume that $p > n$ . For $E \subset R^{n}$ , denote by $L^{m, p} (E)$ the space…

math.CA2012★ 3 cited

Sobolev Extension By Linear Operators

Charles L. Fefferman, Arie Israel, Garving K. Luli

Let $L^{m, p} (R^{n})$ be the Sobolev space of functions with $m^{t h}$ derivatives lying in $L^{p} (R^{n})$ . Assume that $n < p < \infty$ . For $E \subset R^{n}$ , let $L^{m, p} (E)$ denote the…

Semialgebraic Cm solutions to a univariate system of linear inequalities with Nash forcing

Smooth solutions to systems of linear inequalities on R

Optimal C1,1 and Quasi-Optimal C2 Monotone Interpolation with Curvature Control

On Cm Solutions to Systems of Linear Inequalities

Smooth Selection for Infinite Sets

C2 Interpolation with Range Restriction

Algorithms for Nonnegative C2(R2) Interpolation

Cm Semialgebraic Sections Over the Plane

On the Shape Fields Finiteness Principle

C2(R2) Nonnegative Extension by Bounded-depth Operators

Solutions to a System of Equations for Cm Functions

Generators for the Cm-closures of Ideals

Nonnegative C2(R2) interpolation

On one-dimension semi-linear wave equations with null conditions

Interpolation of data by smooth non-negative functions

Finitness Principles for Smooth Selection

Finiteness Principles for Smooth Selection

On the generalized Buckley-Leverett equation

Fitting a Sobolev function to data

The Brenner-Hochster-Kollár and Whitney Problems for Vector-valued Functions and Jets

The Structure of Sobolev Extension Operators

Sobolev Extension By Linear Operators

Semialgebraic $C^{m}$ solutions to a univariate system of linear inequalities with Nash forcing

Smooth solutions to systems of linear inequalities on $R$

Optimal $C^{1, 1}$ and Quasi-Optimal $C^{2}$ Monotone Interpolation with Curvature Control

On $C^{m}$ Solutions to Systems of Linear Inequalities

$C^{2}$ Interpolation with Range Restriction

Algorithms for Nonnegative $C^{2} (R^{2})$ Interpolation

$C^{m}$ Semialgebraic Sections Over the Plane

$C^{2} (R^{2})$ Nonnegative Extension by Bounded-depth Operators

Solutions to a System of Equations for $C^{m}$ Functions

Generators for the $C^{m}$ -closures of Ideals

Nonnegative $C^{2} (R^{2})$ interpolation