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dc.contributor.authorLuef, Franz
dc.contributor.authorWang, Xu
dc.identifier.citationGeometric and Functional Analysis. 2023, 33 (3), 778-823.en_US
dc.description.abstractWe investigate the frame set of regular multivariate Gaussian Gabor frames using methods from Kähler geometry such as Hörmander’s - estimate with singular weight, Demailly’s Calabi–Yau method for Kähler currents and a Kähler-variant generalization of the symplectic embedding theorem of McDuff–Polterovich for ellipsoids. Our approach is based on the well-known link between sets of interpolation for the Bargmann-Fock space and the frame set of multivariate Gaussian Gabor frames. We state sufficient conditions in terms of a certain extremal type Seshadri constant of the complex torus associated to a lattice to be a set of interpolation for the Bargmann-Fock space, and give also a condition in terms of the generalized Buser-Sarnak invariant of the lattice. In particular, we obtain an effective Gaussian Gabor frame criterion in terms of the covolume for almost all lattices, which is the first general covolume criterion in multivariate Gaussian Gabor frame theory. The recent Berndtsson–Lempert method and the Ohsawa–Takegoshi extension theorem also allow us to give explicit estimates for the frame bounds in terms of certain Robin constant. In the one-dimensional case we obtain a sharp estimate of the Robin constant using Faltings’ theta metric formula for the Arakelov Green functions.en_US
dc.publisherSpringer Nature Ltd.en_US
dc.rightsNavngivelse 4.0 Internasjonal*
dc.titleGaussian Gabor frames, Seshadri constants and generalized Buser-Sarnak invariantsen_US
dc.title.alternativeGaussian Gabor frames, Seshadri constants and generalized Buser-Sarnak invariantsen_US
dc.typePeer revieweden_US
dc.typeJournal articleen_US
dc.source.journalGeometric and Functional Analysisen_US

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Navngivelse 4.0 Internasjonal
Except where otherwise noted, this item's license is described as Navngivelse 4.0 Internasjonal