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

2010/03/13 by Waters, Alden
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1003.2747

Abstract

We construct a frame of complex Gaussians for the space of L²(ℝⁿ) 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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