A Gabor system is a set of time-frequency shifts S(g, ) = {e 2πibx g(xa)} (a,b)∈ of a function g ∈ L 2 (R d ). We prove that if a finite union of Gabor systems r k=1 S(g k , k ) forms a frame for L 2 (R d ) then the lower and upper Beurling densities of = r k=1 k satisfy D -( ) ≥ 1 and D + ( ) < ∞.
Frame constants of Gabor frames near the critical density
✍ Scribed by A. Borichev; K. Gröchenig; Yu. Lyubarskii
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 169 KB
- Volume
- 94
- Category
- Article
- ISSN
- 0021-7824
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