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Simultaneous estimates for vector-valued Gabor frames of Hermite functions

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Abstract

We derive frame bound estimates for vector-valued Gabor systems with window functions belonging to Schwartz space. The main result provides estimates for windows composed of Hermite functions. The proof is based on a recently established sampling theorem for the simply connected Heisenberg group, which is translated to a family of frame bound estimates via a direct integral decomposition.

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Authors and Affiliations

  1. Lehrstuhl A für Mathematik, RWTH Aachen, 52056, Aachen, Germany

    H. Führ

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  1. H. Führ
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Correspondence to H. Führ.

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Communicated by Qiyu Sun.

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Führ, H. Simultaneous estimates for vector-valued Gabor frames of Hermite functions. Adv Comput Math 29, 357–373 (2008). https://doi.org/10.1007/s10444-007-9053-4

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  • DOI: https://doi.org/10.1007/s10444-007-9053-4

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