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

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