Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19368120210701On the frames by multiplication and irregular frames of translates on LCA groupsدربارهٔ قابهای ضربی و قاب انتقالات نامنظم روی گروههای موضعاً فشردهٔ آبلی71624522310.22072/wala.2021.130732.1295ENN.S.SeyediDepartment of Pure Mathematics, Ferdowsi University of Mashhad, Iran.M.MortazavizadehDepartment of Pure Mathematics, Ferdowsi University of Mashhad, Iran.R. A.Kamyabi GolDepartment of Pure Mathematics, Ferdowsi University of Mashhad, Iran.Journal Article20200711Let $X$ 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.https://wala.vru.ac.ir/article_245223_ac1d03935a9178a6ee5d0304f9408375.pdf