Fushuai Jiang

activity

20192026

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

Interpolation

8 citations · 9 across the 12 of their papers we have counts for

collaborators

14 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.FA2026

On a family of one-dimensional oscillation inequalities

Fushuai Jiang

Let $φ$ be a nonzero continuous mean-zero function on the one-dimensional torus and let $N_{φ}$ be the number of times that $φ$ changes signs. We prove the sharp family of oscillatio…

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.MG2024

Metric properties of partial and robust Gromov-Wasserstein distances

Jannatul Chhoa, Michael Ivanitskiy, Fushuai Jiang +4

The Gromov-Wasserstein (GW) distances define a family of metrics, based on ideas from optimal transport, which enable comparisons between probability measures defined on distinct m…

math.FA2024

Factorization of positive-semidefinite operators with absolutely summable entries

Radu Balan, Fushuai Jiang

A problem by Feichtinger, Heil, and Larson asks whether every infinite matrix $A$ with $\sum_{k, l} ∣ A_{k l} ∣ < \infty$ (an equivalent substitute for the Feichtinger algebra) that is…

math.FA2023

Roots, trace, and extendability of flat nonnegative smooth functions

Fushuai Jiang

Building on the univariate techniques developed by Ray and Schmidt-Hieber, we study the class $F^{s} (R^{n})$ of multivariate nonnegative smooth functions that are su…

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.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

Nonnegative Whitney Extension Problem for $C^{1} (R^{n})$

Fushuai Jiang

Let $f$ be a real-valued function on a compact subset in $R^{n}$ . We show how to decide if $f$ extends to a nonnegative and $C^{1}$ function on $R^{n}$ . There…

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…

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

On a family of one-dimensional oscillation inequalities

Smooth solutions to systems of linear inequalities on R

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

Metric properties of partial and robust Gromov-Wasserstein distances

Factorization of positive-semidefinite operators with absolutely summable entries

Roots, trace, and extendability of flat nonnegative smooth functions

Smooth Selection for Infinite Sets

C2 Interpolation with Range Restriction

Algorithms for Nonnegative C2(R2) Interpolation

On the Shape Fields Finiteness Principle

C2(R2) Nonnegative Extension by Bounded-depth Operators

Nonnegative Whitney Extension Problem for C1(Rn)

Nonnegative C2(R2) interpolation

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

$C^{2}$ Interpolation with Range Restriction

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

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

Nonnegative Whitney Extension Problem for $C^{1} (R^{n})$

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