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arXiv · 1003.2747

A Parametrix Construction for the Wave Equation with Low Regularity Coefficients Using a Frame of Gaussians

Alden Waters
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Abstract

We construct a frame of complex Gaussians for the space of $L^2(\mathbb{R}^n)$ functions. When propagated along bicharacteristics for the wave equation, the frame can be used to build a parametrix with suitable error terms. When the coefficients of the wave equation have more regularity, propagated frame functions become Gaussian beams.

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Alden Waters. 2010-03-18. A Parametrix Construction for the Wave Equation with Low Regularity Coefficients Using a Frame of Gaussians. https://arxiv.org/abs/1003.2747

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