%0 Journal Article %T On the frames by multiplication and irregular frames of translates on LCA groups %J Wavelet and Linear Algebra %I Vali-e-Asr university of Rafsanjan %Z 2383-1936 %A Seyedi, N.S. %A Mortazavizadeh, M. %A Kamyabi Gol, R. A. %D 2021 %\ 07/01/2021 %V 8 %N 1 %P 7-16 %! On the frames by multiplication and irregular frames of translates on LCA groups %K locally compact abelian group %K frame by multiplication %K irregular frame of translates %R 10.22072/wala.2021.130732.1295 %X 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 $L^2(E)$. Also, we study the equivalent conditions for a system of translates to be a Bessel family in $L^2(G)$ 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. %U https://wala.vru.ac.ir/article_245223_ac1d03935a9178a6ee5d0304f9408375.pdf