@ARTICLE{Osgooei, author = {Osgooei, E. and }, title = {New Approaches to Duals of Fourier-like Systems}, volume = {13}, number = {2}, abstract ={‎The sequences of the form ${E_{mb}g_{n}}_{m‎, ‎ninmathbb{Z}}$,‎ ‎where $E_{mb}$ is the modulation operator‎, ‎$b>0$ and $g_{n}$ is the‎ ‎window function in $L^{2}(mathbb{R})$‎, ‎construct Fourier-like‎ ‎systems‎. ‎We try to consider some sufficient conditions on the window‎ ‎functions of Fourier-like systems‎, ‎to make a frame and find a dual‎ ‎frame with the same structure‎. ‎We also extend the given two Bessel‎ ‎Fourier-like systems to make a pair of dual frames and prove that‎ ‎the window functions of Fourier-like Bessel sequences share the‎ ‎compactly supported property with their extensions‎. ‎But for‎ ‎polynomials windows‎, ‎a result of this type does not happen. }, URL = {http://ijmsi.ir/article-1-729-en.html}, eprint = {http://ijmsi.ir/article-1-729-en.pdf}, journal = {Iranian Journal of Mathematical Sciences and Informatics}, doi = {}, year = {2018} }