@article { author = {Seyedi, N.S. and Mortazavizadeh, M. and Kamyabi Gol, R. A.}, title = {On the frames by multiplication and irregular frames of translates on LCA groups}, journal = {Wavelet and Linear Algebra}, volume = {8}, number = {1}, pages = {7-16}, year = {2021}, publisher = {Vali-e-Asr university of Rafsanjan}, issn = {2383-1936}, eissn = {2476-3926}, doi = {10.22072/wala.2021.130732.1295}, abstract = {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.}, keywords = {locally compact abelian group,frame by multiplication,irregular frame of translates}, title_fa = {دربارهٔ قاب‌های ضربی و قاب انتقالات نامنظم روی گروه‌های موضعاً فشردهٔ آبلی}, abstract_fa = {}, keywords_fa = {}, url = {https://wala.vru.ac.ir/article_245223.html}, eprint = {https://wala.vru.ac.ir/article_245223_ac1d03935a9178a6ee5d0304f9408375.pdf} }