Luo, Shunlong Deforming Gabor frames by quadratic Hamiltonians. (English) Zbl 0962.44008 Integral Transforms Spec. Funct. 9, No. 1, 69-74 (2000). 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. Cited in 3 Documents MSC: 44A15 Special integral transforms (Legendre, Hilbert, etc.) 47B38 Linear operators on function spaces (general) 81R30 Coherent states Keywords:Gabor frames; Bargmann representation; quadratic Hamiltonian; Wick symbol; Weyl operators; Heisenberg algebra; integral transforms; Fock space PDFBibTeX XMLCite \textit{S. Luo}, Integral Transforms Spec. Funct. 9, No. 1, 69--74 (2000; Zbl 0962.44008) Full Text: DOI References: [1] DOI: 10.1002/cpa.3160140303 · Zbl 0107.09102 · doi:10.1002/cpa.3160140303 [2] Berezin F.A., Math. sb. 86 pp 578– (1971) [3] Folland G.B., Harmonic Analysis in Phase Space (1989) · Zbl 0682.43001 [4] DOI: 10.1063/1.530594 · Zbl 0813.46062 · doi:10.1063/1.530594 [5] Klauder J.R., Coherent States (1985) [6] DOI: 10.1016/S0034-4877(97)88004-4 · Zbl 0892.47069 · doi:10.1016/S0034-4877(97)88004-4 [7] DOI: 10.1017/S0013091500013870 · Zbl 0005.13203 · doi:10.1017/S0013091500013870 [8] Perelomov A., Generalized Coherent States and Their Applications (1986) · Zbl 0605.22013 [9] DOI: 10.1515/crll.1992.429.91 · Zbl 0745.46034 · doi:10.1515/crll.1992.429.91 [10] Seip K., J. Rein. Angew. Math. 429 pp 107– (1992) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.