Gabor Wave Packets and Evolution Operators
We perform a Gabor analysis for a large class of evolution equations with constant coefficients. We show that the corresponding propagators have a very sparse Gabor matrix, displaying off-diagonal exponential decay. The results apply to hyperbolic, weakly hyperbolic and parabolic equations. Some numerical experiments are provided.
KeywordsPseudodifferential operators Gelfand–Shilov spaces short-time Fourier transform Gabor frames sparse representations hyperbolic equations parabolic equations
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