Xiaohua Yao

activity

20212026

collaborators

14 papers

cs.AI2026

LAGO: Language Agents with Reusable Growing Options

Yuran Wu, Mengkang Hu, Qionglin Qiu +5

Long-horizon tasks expose a weakness of monolithic tool-use loops: one agent must decompose, execute, and verify a task within a single trajectory. We introduce LAGO, which treats…

math.AP2026

Endpoint Mapping Properties of Wave Operators for Schrödinger Operators in Dimensions $n \geq 3$

Han Cheng, Changxing Miao, Xiaohua Yao

We study endpoint mapping properties of low-energy wave operators for Schrödinger operators $H = - Δ + V$ on $R^{n}$ , $n \geq 3$ . In dimension four, we prove that a zero-energy reson…

math.AP2026

Endpoint Mapping Properties of Wave Operators for Two-Dimensional Schrödinger Operators

Han Cheng, Changxing Miao, Xiaohua Yao

We establish sharp endpoint mapping properties for the wave operators $W_{\pm} (H, - Δ)$ of two-dimensional Schrödinger operators $H = - Δ + V$ with real-valued decaying potentials $V$ . Toge…

math.AP2026

Time-Decay Estimates for Two-Dimensional Fourth-Order Schrödinger Operators with Threshold Singularities

Zijun Wan, Xiaohua Yao

We establish time-decay estimates for the two-dimensional fourth-order Schrödinger operator $H = Δ^{2} + V$ with a real-valued decaying potential $V$ , covering all possible zero-energy t…

math.AP2026

Decay estimates for the two-dimensional Beam equation with potentials

Shuangshuang Chen, Han Cheng, Zijun Wan +1

This paper establishes time decay estimates for the following two-dimensional beam (plate) equation with a decaying real-valued potential $V$ : \begin{equation*} \partial_t^2 u + (Δ…

math.AP2025

The $ℓ^{p}$ -boundedness of wave operators for the fourth order Schrödinger operators on the lattice $Z$

Sisi Huang, Xiaohua Yao

This paper investigates the $ℓ^{p}$ boundedness of wave operators $W_{\pm} (H, Δ^{2})$ associated with discrete fourth-order Schrödinger operators $H = Δ^{2} + V$ on the lattice $\mathbb{…

math.AP2025

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $Z$

Sisi Huang, Xiaohua Yao

It is known that the discrete Laplace operator $Δ$ on the lattice $Z$ satisfies the following sharp time decay estimate: $$\big\|e^{itΔ}\big\|_{\ell^1\rightarrow\ell^{\inf…

math.AP2025

The $L^{p}$ -boundedness of wave operators for higher order Schrödinger operator with zero singularities in low odd dimensions

Han Cheng, Avy Soffer, Zhao Wu +1

This paper investigates the $L^{p}$ -bounds of wave operators for higher-order Schrödinger operators $H = (- Δ)^{m} + V$ on $R^{n}$ , with $m \geq 2$ and real-valued decaying potent…

math.AP2025

The $L^{p}$ -boundedness of wave operators for nonhomogeneous fourth-order Schrödinger operators in high dimensions

Zijun Wan, Xiaohua Yao

This paper investigates the $L^{p}$ -boundedness of wave operators associated with the nonhomogeneous fourth-order Schödinger operator $H = Δ^{2} - Δ + V (x)$ on $R^{n}$ . Assuming…

math.AP2025

Decay estimates for discrete bi-Schrödinger operators on the lattice $Z$

Sisi Huang, Xiaohua Yao

It is known that the discrete Laplace operator $Δ$ on the lattice $Z$ satisfies the following sharp time decay estimate: $$\left\|e^{itΔ}\right\|_{\ell^1\rightarrow\ell^{\…

math.AP2024

Decay estimates for beam equations with potentials on the line

Shuangshuang Chen, Zijun Wan, Xiaohua Yao

This paper is devoted to the time decay estimates for the following beam equation with a potential on the line: $$ \partial_t^2 u + \left( Δ^2 + m^2 + V(x) \right) u = 0, \ \ u(0,…

math.AP2023

Counterexamples and weak (1,1) estimates of wave operators for fourth-order Schrödinger operators in dimension three

Haruya Mizutani, Zijun Wan, Xiaohua Yao

This paper is dedicated to investigating the $L^{p}$ -bounds of wave operators $W_{\pm} (H, Δ^{2})$ associated with fourth-order Schrödinger operators $H = Δ^{2} + V$ on $R^{3}$ . We consid…

math.AP2023

$L^{p}$ -boundedness of wave operators for fourth order Schrödinger operators with zero resonances on $R^{3}$

Haruya Mizutani, Zijun Wan, Xiaohua Yao

Let $H = Δ^{2} + V$ be the fourth-order Schrödinger operator on $R^{3}$ with a real-valued fast-decaying potential $V$ . If zero is neither a resonance nor an eigenvalue of $H$ …

math.AP2021

Decay estimates for fourth-order Schrödinger operators in dimension two

Ping Li, Avy Soffer, Xiaohua Yao

In this paper we study the decay estimates of the fourth order Schrödinger operator $H = Δ^{2} + V (x)$ on $R^{2}$ with a bounded decaying potential $V (x)$ . We first deduce the a…

LAGO: Language Agents with Reusable Growing Options

Endpoint Mapping Properties of Wave Operators for Schrödinger Operators in Dimensions n≥3

Endpoint Mapping Properties of Wave Operators for Two-Dimensional Schrödinger Operators

Time-Decay Estimates for Two-Dimensional Fourth-Order Schrödinger Operators with Threshold Singularities

Decay estimates for the two-dimensional Beam equation with potentials

The ℓp-boundedness of wave operators for the fourth order Schrödinger operators on the lattice Z

Decay estimates for discrete bi-Laplace operators with potentials on the lattice Z

The Lp-boundedness of wave operators for higher order Schrödinger operator with zero singularities in low odd dimensions

The Lp-boundedness of wave operators for nonhomogeneous fourth-order Schrödinger operators in high dimensions

Decay estimates for discrete bi-Schrödinger operators on the lattice Z

Decay estimates for beam equations with potentials on the line

Counterexamples and weak (1,1) estimates of wave operators for fourth-order Schrödinger operators in dimension three

Lp-boundedness of wave operators for fourth order Schrödinger operators with zero resonances on R3

Decay estimates for fourth-order Schrödinger operators in dimension two

Endpoint Mapping Properties of Wave Operators for Schrödinger Operators in Dimensions $n \geq 3$

The $ℓ^{p}$ -boundedness of wave operators for the fourth order Schrödinger operators on the lattice $Z$

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $Z$

The $L^{p}$ -boundedness of wave operators for higher order Schrödinger operator with zero singularities in low odd dimensions

The $L^{p}$ -boundedness of wave operators for nonhomogeneous fourth-order Schrödinger operators in high dimensions

Decay estimates for discrete bi-Schrödinger operators on the lattice $Z$

$L^{p}$ -boundedness of wave operators for fourth order Schrödinger operators with zero resonances on $R^{3}$