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

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

2010-03-13

arxiv.org/abs/1003.2747v2

Mathematics

Analysis of PDEs

Scientific paper

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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