Avy Soffer is a professor at the Department of Mathematics, Rutgers University. He obtained his PhD at Tel-Aviv University in Mathematical-Physics in 1984. He was a Sloan fellow in 1988, ICM invited speaker in 2006,  and AMS Fellow in 2015.Chris Stucchio is a product-focused data science and engineering researcher. He obtained his PhD at Rutgers University. Minh-Binh Tran is a faculty in the mathematics department of Texas A&M University, USA. He obtained a PhD in applied mathematics at Université Sorbonne Paris Nord, France. He was a recipient of the NSF CAREER Award in 2021 and was a Humboldt Fellow in 2021.

• Introduction.- Absorbing Potentials and Perfectly Matched Layers.- Windowed Fourier Transforms and Space Phase Numerics.- Description of Time Dependent Phase Space Filters.- A More Practical Discussion: How to Choose the Parameters.- The Behavior of Gaussian Framelets under the Free Flow.- Assumptions and Accuracy Estimates.- Discussions on the Assumptions.- Proof of Theorem 7.5.6.- Proof of Theorems 7.5.4 and 7.5.5.- Numerical Experiments.