Properties of Gabor multipliers and frames for physical modeling

We present techniques developed for numerical modeling of wave propagation, and source-signature removal in seismic imaging, based on a class of linear operators known as Gabor multipliers. These operators are localized Fourier multipliers, whose actions are selectively localized by an element of a partition of unity. Using generalized frames, we prove boundedness and stability properties for these operators, and indicate how to model PDEs and pseudodifferential operators, and an approximate functional calculus.