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Deficits and Excesses of Frames |
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| Authors: | Radu Balan Peter G Casazza Christopher Heil Zeph Landau |
| Institution: | (1) Siemens Corporate Research, Princeton, NJ 08540, USA;(2) Department of Mathematics, University of Missouri, Columbia, MO 65211, USA;(3) School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA;(4) Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, CA 94720, USA |
| Abstract: | The excess of a sequence in a Hilbert space is the greatest number of elements that can be removed yet leave a set with the same closed span. We study the excess and the dual concept of the deficit of Bessel sequences and frames. In particular, we characterize those frames for which there exist infinitely many elements that can be removed from the frame yet still leave a frame, and we show that all overcomplete Weyl–Heisenberg and wavelet frames have this property. |
| Keywords: | Bessel sequences deficit excess frames Gabor systems Riesz bases wavelets Weyl– Heisenberg systems |
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