Andrew Walton Green

I currently work in the harmonic analysis group at Washington University in St. Louis, where my postdoctoral mentor is Brett Wick. In May 2020, I received my PhD in Mathematical Sciences from Clemson University under the direction of Shitao Liu and Mishko Mitkovski. My research interests are in harmonic analysis and its applications to PDEs, specifically control theory and quasiconformal regularity.

Papers

On the dimension of observable sets for the heat equation

with Kévin Le Balc'h, Jérémy Martin, and Marcu-Antone Orsoni

submitted. arXiv

Multilinear paraproducts on Sobolev spaces

with Francesco Di Plinio and Brett D. Wick

Boll. Unione Mat. Ital. (2024). arXiv journal

Multilinear wavelet compact T(1) theorem

with Anastasios Fragkos and Brett D. Wick

submitted. arXiv

Quantitative Sobolev regularity of quasiregular maps

with Francesco Di Plinio and Brett D. Wick

submitted. arXiv

Wavelet resolution and Sobolev regularity of Calderón-Zygmund forms on domains

with Francesco Di Plinio and Brett D. Wick

submitted. arXiv

Weighted estimates for the Bergman projection on planar domains

with Nathan A. Wagner

Trans. Amer. Math. Soc. 377, No. 11 (2024) arXiv journal

Dominating sets in Bergman spaces on strongly pseudoconvex domains

with Nathan A. Wagner

Constr. Approx. 59, (2024) arXiv journal

Invertibility of positive Toeplitz operators and associated uncertainty principle

with Mishko Mitkovski

J. Fourier Anal. Appl. 29, No. 4 (2023) arXiv journal

Bilinear wavelet representation of Calderón-Zygmund forms

with Francesco Di Plinio and Brett D. Wick

Pure Appl. Anal. 5, No. 1 (2023) arXiv journal

Source reconstruction and stability via boundary control of abstract viscoelastic systems

with Shitao Liu

Appl. Anal. 101, No. 14 (2022) arXiv journal

Uncertainty principles associated to sets satisfying the geometric control condition

with Benjamin Jaye and Mishko Mitkovski

J. Geom. Anal. 32, No. 3 (2022) arXiv journal

On the energy decay rate of the fractional wave equation on ℝ with relatively dense damping

Proc. Amer. Math. Soc. 148, No. 11 (2020). arXiv journal

Boundary observability of a visco-elastic wave equation

with Shitao Liu and Mishko Mitkoski

SIAM J. Control Optim. 57, No. 3 (2019). PDF journal

Presentations

• Local and global Sobolev regularity of quasiconformal maps
• Sobolev regularity of singular integral operators on domains
• Bilinear wavelet representation of CZ forms (video)
• Dominating sets in Bergman spaces on domains (video)
• Positivity of some Toeplitz operators
• On the energy decay rate of the fractional wave equation with relatively dense damping
• Control theory for PDEs and uncertainty principles
• Control and inverse problem for viscoelastic wave equation