TY - JOUR ID - 245223 TI - On the frames by multiplication and irregular frames of translates on LCA groups JO - Wavelet and Linear Algebra JA - WALA LA - en SN - 2383-1936 AU - Seyedi, N.S. AU - Mortazavizadeh, M. AU - Kamyabi Gol, R. A. AD - Department of Pure Mathematics, Ferdowsi University of Mashhad, Iran. Y1 - 2021 PY - 2021 VL - 8 IS - 1 SP - 7 EP - 16 KW - locally compact abelian group KW - frame by multiplication KW - irregular frame of translates DO - 10.22072/wala.2021.130732.1295 N2 - 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. UR - https://wala.vru.ac.ir/article_245223.html L1 - https://wala.vru.ac.ir/article_245223_ac1d03935a9178a6ee5d0304f9408375.pdf ER -