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Deforming Gabor frames by quadratic Hamiltonians. (English) Zbl 0962.44008

Summary: In quantum mechanical Heisenberg algebra, evolutions generated by quadratic Hamiltonians are unitary integral transforms on Fock space. By deforming Gabor frames along these evolutions, we obtain a wide class of Gabor frames with the same frame bounds. Of particular examples are rotations and squeezings.

MSC:

44A15 Special integral transforms (Legendre, Hilbert, etc.)
47B38 Linear operators on function spaces (general)
81R30 Coherent states
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