Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک
IJMSI
Basic Sciences
http://ijmsi.ir
1
admin
1735-4463
2008-9473
8
10.61186/ijmsi
14
8888
13
en
jalali
1397
7
1
gregorian
2018
10
1
13
2
online
1
fulltext
en
New Approaches to Duals of Fourier-like Systems
تخصصي
Special
پژوهشي
Research paper
‎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.
Fourier-like systems, Shift-invariant systems, A pair of dual frames, Polynomials.
15
27
http://ijmsi.ir/browse.php?a_code=A-10-1442-1&slc_lang=en&sid=1
E.
Osgooei
e.osgooei@uut.ac.ir
10031947532846006503
10031947532846006503
Yes
Department of Sciences, Urmia University of Technology, Urmia, Iran.