f. esmaeelzadeh

In this paper, we consider some kinds of semiregular frames of translates on the Hilbert space L 2 (R d ). More precisely, we investigate the frames of the form {TAkf}k∈Zd where A is a real invertible d × d matrix, f ∈ L 2 (R d ) and it is a frame for the closed subspace generated by {TAkf}k∈Zd .

Let $H$ and $K$ be compact subgroups of locally compact group $G$. By considering the double coset space $Ksetminus G/H$, which equipped with an $N$-strongly quasi invariant measure $mu$, for $1leq pleq +infty$, we make a norm decreasing linear map from $L^p(G)$ onto $L^p(Ksetminus G/H,mu)$ and demonstrate that it may be identified with a quotient space of $L^p(G)$. In addition, we illustrate that $L^p(Ksetminus G/H, mu)$ is isometrically isomorphic to a closed subspace of $L^p(G)$. These assist us to study the structure of the classical Banach space created on a double coset space by those produced on topological space.