Simultaneous estimates for vector-valued Gabor frames of Hermite functions |
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Authors: | H Führ |
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Institution: | (1) Lehrstuhl A für Mathematik, RWTH Aachen, 52056 Aachen, Germany |
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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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Keywords: | Gabor frames Hermite functions Heisenberg group Paley– Wiener space Sampling theorems Direct integral decomposition |
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