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

Analysis Seminar
Wednesday, November 28, 2012 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005
Alden Waters – Jyvaskyla University
Michael Lacey
We show how to construct frames for square integrable functionsout of modulated Gaussians. Using the frame representation of the Cauchydata, we show that we can build a suitable approximation to the solutionfor low regularity, time dependent wave equations. The talk will highlightthe relationship of the construction to harmonic analysis and will explorethe differences of the new construction to the standard Gaussian beamansatz.