Alden Waters: A parametrix construction for the wave equation with low regularity coefficients using a frame of gaussians

We show how to construct frames for square integrable functions out of modulated Gaussians. Using the frame representation of the Cauchy data, we show that we can build a suitable approximation to the solution for low regularity, time dependent wave equations. The talk will highlight the relationship of the construction to inverse problems and will explore the differences of the new construction to the standard Gaussian beam Ansatz.