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On a necessary condition for B-spline Gabor frames

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Abstract

In a previous note Gröchenig et al. prove that if g is a continuous function with compact support such that the translates of g form a partition of unity, then g cannot generate a Gabor frame for integer values of the frequency shift parameter b greater than 1 (Gröchenig et al. in IEEE Trans Inform Theory 49:3318–3320, 2003). We give a simpler proof of this result which applies also to windows g which are neither continuous nor with compact support. Our proof is based on a necessary condition for Gabor frames due to Heil and Walnut.

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  1. Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146, Genova, Italy

    Vincenza Del Prete

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  1. Vincenza Del Prete
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Correspondence to Vincenza Del Prete.

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Communicated by G. Talenti.

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Del Prete, V. On a necessary condition for B-spline Gabor frames. Ricerche mat. 59, 161–164 (2010). https://doi.org/10.1007/s11587-010-0077-6

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  • DOI: https://doi.org/10.1007/s11587-010-0077-6

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