Density of frames and Schauder bases of windowed exponentials

Heil, Christopher und Kutyniok, Gitta (2008): Density of frames and Schauder bases of windowed exponentials. In: Houston Journal of Mathematics, Vol. 34, No. 2: pp. 565-600

Abstract

This paper proves that every frame of windowed exponentials satises 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 satised by frames of windowed expo- nentials with one or nitely 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0362-1588