arXiv subjects
Publications and source records attributed to M. Mortazavizadeh.
For a locally compact abelian group $\textbf{R}$ with a uniform lattice $Λ$ and a group $G$ that acts on $\textbf{R}$ by continuous automorphisms, we study operators commuting with the representation of $G \rtimes Λ$ on $L^2(\textbf{R})$. As a consequence, we give a characterization of shift-dilation preserving operators.
We study translation preserving operators, that is operators commuting with translations by a closed subgroup of a locally compact abelian group. We show that there is a one to one correspondence between these operators and range operators. Furthermore, we obtain a necessary condition for a translation preserving operator to be Hilbert Schmidt or of finite trace in terms of its range operator.
Let $G$ be a locally compact abelian group and $Λ$ be a closed subgroup of the dual group $\widehat{G}$. In this paper, we investigate modulation preserving operators with respect to $Λ$, and give a characterization of them in terms of range operators.
We define and investigate modulation invariant spaces on a locally compact abelian group $G$ with respect to a closed subgroup of the dual group $\widehat{G}$. Using a range function approach, we establish a characterization of modulation invariant spaces. Finally, we define a metric on the collection of all modulation invariant spaces and study some topological properties of the metric space.