On the frames by multiplication and irregular frames of translates on LCA groups

Let X be a measure space and let E be a measurable subset of X with finite positive measure. In this paper, we investigate frame and Riesz basis properties of a family of functions multiplied by another measurable function in L^۲(E). Also, we study the equivalent conditions for a system of translates to be a Bessel family in L^۲(G) and to be a frame for P_E (the space of the band limited functions). Finally, we study the properties of frames of translates that preserved by convolution.