Density of frames and Schauder bases of windowed exponentials

• Autores: Christopher Heil, Gitta Kutyniok
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 34, Nº 2, 2008, págs. 565-600
• Idioma: inglés
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• Resumen

  • This paper proves that every frame of windowed exponentials satisfies a Strong Homogeneous Approximation Property with respect to its canonical dual frame, and a Weak Homogeneous Approximation Property with respect to an arbitrary dual frame. As a consequence, a simple proof of the Nyquist density phenomenon satisfied by frames of windowed exponentials with one or finitely many generators is obtained. The more delicate cases of Schauder bases and exact systems of windowed exponentials are also studied. New results on the relationship between density and frame bounds for frames of windowed exponentials are obtained. In particular, it is shown that a tight frame of windowed exponentials must have uniform Beurling density.