Frames of multi-windowed exponentials on subsets of Rd

@inproceedings{Gabardo2014FramesOM,
  title={Frames of multi-windowed exponentials on subsets of Rd},
  author={Jean-Pierre Gabardo and Chun-Kit Lai},
  year={2014}
}
Abstract Given discrete subsets Λ j ⊂ R d , j = 1 , … , q , consider the set of windowed exponentials ⋃ j = 1 q { g j ( x ) e 2 π i 〈 λ , x 〉 : λ ∈ Λ j } on L 2 ( Ω ) . We show that a necessary and sufficient condition for the windows g j to form a frame of windowed exponentials for L 2 ( Ω ) with some Λ j is that 0 m ⩽ max j ∈ J | g j | ⩽ M almost everywhere on Ω for some subset J of { 1 , … , q } . If Ω is unbounded, we show that there is no frame of windowed exponentials if the Lebesgue… CONTINUE READING