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FRAME OPERATORS AND SEMI-FRAME OPERATORS OF FINITE GABOR FRAMES
( N. M. Madhavan Namboothiri ),( T. C. Easwaran Nambudiri ),( Jineesh Thomas ) 한국수학교육학회 2021 純粹 및 應用數學 Vol.28 No.4
A characterization of frame operators of finite Gabor frames is presented here. Regularity aspects of Gabor frames in l<sup>2</sup>(Z<sub>N</sub>) are discussed by introducing associated semi-frame operators. Gabor type frames in finite dimensional Hilbert spaces are also introduced and discussed.
Jayaprasad, PN,Madhavan, Namboothiri NM,Santhosh, PK,Varghese, Jacob The Kangwon-Kyungki Mathematical Society 2021 한국수학논문집 Vol.29 No.3
Every closed subset of a compact topological space is compact. Also every compact subset of a Hausdorff topological space is closed. It follows that compact subsets are precisely the closed subsets in a compact Hausdorff space. It is also proved that a topological space is maximal compact if and only if its compact subsets are precisely the closed subsets. A locale is a categorical extension of topological spaces and a frame is an object in its opposite category. We investigate to find whether the closed sublocales are exactly the compact sublocales of a compact Hausdorff frame. We also try to investigate whether the closed sublocales are exactly the compact sublocales of a maximal compact frame.
Gabor frames in l²(R) from Gabor frames in l²(R)
Jineesh Thomas,Madhavan Namboothiri N M,Eldo Varghese 강원경기수학회 2020 한국수학논문집 Vol.28 No.4
In this paper we discuss about the image of Gabor frame under a unitary operator and derive a sufficient condition under which a unitary operator from $L^2 (\mathbb R)$ to $l^2 (\mathbb Z)$ maps Gabor frame in $L^2 (\mathbb R)$ to a Gabor frame in $l^2 (\mathbb Z)$.
Generalized pseudo $B$-Gabor frames on finite abelian groups
Jineesh Thomas,Madhavan Namboothiri N M 강원경기수학회 2024 한국수학논문집 Vol.32 No.1
We seek for an invertible map $B$ from $L^2(\Gamma)$ to $L^2(G)$, where $G$ is a finite abelian group and $\Gamma$ is the direct product of finite cyclic groups which is isomorphic to $G$, so that any Gabor frame in $L^2(G)$, is a generalized pseudo $B$-Gabor frame.
A Class of Structured Frames in Finite Dimensional Hilbert Spaces
Jineesh Thomas,N. M. Madhavan Namboothiri,T. C. Easwaran Nambudiri 한국수학교육학회 2022 純粹 및 應用數學 Vol.29 No.4
We introduce a special class of structured frames having single generators in finite dimensional Hilbert spaces. We call them as pseudo B-Gabor like frames and present a characterisation of the frame operators associated with these frames. The concept of Gabor semi-frames is also introduced and some significant properties of the associated semi-frame operators are discussed.