TY - JOUR JF - IJMSI JO - IJMSI VL - 13 IS - 2 PY - 2018 Y1 - 2018/10/01 TI - New Approaches to Duals of Fourier-like Systems TT - N2 - ‎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. SP - 15 EP - 27 AU - Osgooei, E. AD - Department of Sciences, Urmia University of Technology, Urmia, Iran. KW - Fourier-like systems KW - Shift-invariant systems KW - A pair of dual frames KW - Polynomials. UR - http://ijmsi.ir/article-1-729-en.html ER -