Density results for subspace multiwindow Gabor systems in the rational case.

Let $$\mathbb{S}$$ be a periodic set in ℝ and $$L^2 \left( \mathbb{S} \right)$$ be a subspace of L(ℝ). This paper investigates the density problem for multiwindow Gabor systems in $$L^2 \left( \mathbb{S} \right)$$ for the case that the product of timefrequency shift parameters is a rational number. We derive the density conditions for a multiwindow Gabor system to be complete (a frame) in $$L^2 \left( \mathbb{S} \right)$$. Under such conditions, we construct a multiwindow tight Gabor frame for $$L^2 \left( \mathbb{S} \right)$$ with window functions being characteristic functions. We also provide a characterization of a multiwindow Gabor frame to be a Riesz basis for $$L^2 \left( \mathbb{S} \right)$$, and obtain the density condition for a multiwindow Gabor Riesz basis for $$L^2 \left( \mathbb{S} \right)$$. [ABSTRACT FROM AUTHOR]