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 - http://wala.vru.ac.ir/article_245223.html
L1 - http://wala.vru.ac.ir/article_245223_ac1d03935a9178a6ee5d0304f9408375.pdf
ER -