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arXiv · 1703.02797

Generalized Mehler formula for time-dependent non-selfadjoint quadratic operators and propagation of singularities

Karel Pravda-Starov
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Abstract

We study evolution equations associated to time-dependent dissipative non-selfadjoint quadratic operators. We prove that the solution operators to these non-autonomous evolution equations are given by Fourier integral operators whose kernels are Gaussian tempered distributions associated to non-negative complex symplectic linear transformations, and we derive a generalized Mehler formula for their Weyl symbols. Some applications to the study of the propagation of Gabor singularities (characterizing the lack of Schwartz regularity) for the solutions to non-autonomous quadratic evolution equations are given.

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Karel Pravda-Starov. 2017-03-08. Generalized Mehler formula for time-dependent non-selfadjoint quadratic operators and propagation of singularities. https://arxiv.org/abs/1703.02797

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