4 citations · 5 across the 6 of their papers we have counts for
6 papers
Observability of Schrödinger equations in Euclidean space
Walton Green, Perry Kleinhenz
In this paper we introduce a new dynamical condition, the comb geometric control condition, which is sufficient for observability of the Schrödinger equation in Euclidean space. We…
Bilinear Wavelet Representation of Calderón-Zygmund Forms
Francesco Di Plinio, A. Walton Green, Brett D. Wick
We represent a bilinear Calderón-Zygmund operator at a given smoothness level as a finite sum of cancellative, complexity zero operators, involving smooth wavelet forms, and contin…
Source Reconstruction and Stability via Boundary Control of Abstract Viscoelastic Systems
Walton Green, Shitao Liu
We study the inverse source problem for a class of viscoelastic systems from a single boundary measurement in a general spatial dimension. We give specific reconstruction formula a…
Uncertainty Principles Associated to Sets Satisfying the Geometric Control Condition
Walton Green, Benjamin Jaye, Mishko Mitkovski
In this paper, we study forms of the uncertainty principle suggested by problems in control theory. We obtain a version of the classical Paneah-Logvinenko-Sereda theorem for the an…
On the Energy Decay Rate of the Fractional Wave Equation on with Relatively Dense Damping
Walton Green
We establish upper bounds for the decay rate of the energy of the damped fractional wave equation when the averages of the damping coefficient on all intervals of a fixed length ar…
A Harmonic Analysis Proof of the Boundary Observability Inequality for the Wave Equation and Visco-Elastic Equation
Walton Green, Shitao Liu, Mishko Mitkovski
In this paper, we give a harmonic analysis proof of the Neumann boundary observability inequality for the wave equation in an arbitrary space dimension. Our proof is elementary in…