Hilbert space valued Gabor frames in weighted amalgam spaces

Let H be a separable Hilbert space. In this paper, we establish a generalization of Walnut's representation and Janssen's representation of the H-valued Gabor frame operator on H-valued weighted amalgam spaces WH(Lp, Lqv ), 1 ≤ p, q ≤ ∞. Also, we show that the frame operator is invertible on WH(Lp, Lqv ), 1 ≤ p, q ≤ ∞, if the window function is in the Wiener amalgam space WH(L∞, L1 w). Further, we obtain the Walnut representation and invertibility of the frame operator corresponding to Gabor superframes and multiwindow Gabor frames on WH(Lp, Lqv ), 1 ≤ p, q ≤ ∞, as a special case by choosing the appropriate Hilbert space H.