본문 바로가기
KERD
논문KCI 등재

Generalized pseudo $B$-Gabor frames on finite abelian groups

Jineesh Thomas|Madhavan Namboothiri N M
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2024.03|한국수학논문집 (Korean Journal of Mathematics)|제32권 제1호|pp. 1-14

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

Gabor framesemi-frame operatorfinite abelian groupsframe operator$B$-translation$B$-modulation
주제분류수학

초록

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.

Abstract

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.

참고문헌 (15)

  1. P. G. Cazassa, "Finite Frames Theory and Applications" (2013), Birkhauser
  2. O. Christensen, "An Introduction to Frames and Riesz Bases" (2016), Birkhauser
  3. I. Daubechies, "Painless nonorthogonal expansions", J. Math. Phys, 27, pp.1271~1283 (1986)[DOI]
  4. R. J. Dun, "A class of non-harmonic Fourier series", Trans. Amer. Math. Soc, 72, pp.341~366 (1952)[DOI]
  5. T. C. Easwaran Nambudiri, "Generalized Weyl-Heisenberg frame operators", Bull. Sci. Math., 136, pp.44~53 (2012)[DOI]
  6. T. C. Easwaran Nambudiri, "Characterization of Weyl-Heisenberg frame op-erators", Bull. Sci. Math, 137, pp.322~324 (2013)[DOI]
  7. H. G. Feichtinger, "Gabor Analysis and Algorithms: Theory and Applications", pp.233~266 (1998), Birkhauser
  8. H. G. Feichtinger, "Gabor analysis over nite abelian groups", Appl. Comput. Harmon. Anal, 26(2), pp.230~248 (2009)[DOI]
  9. D. Gabor, "Theory of communication", J. IEE, 93, pp.429~457 (1946)
  10. K. Grochenig, "Foundations of Time Frequency Analysis" (2001), Birkhauser
  11. M. Janssen, "Gabor representation of generalized functions", J. Math. Anal. Appl, 83, pp.377~394 (1981)[DOI]
  12. K. D. Lamb, "Unitary and nonunitary approaches in quantum eld theory", Faculty publications - Physics, 40 (2007)
  13. G. Pfander, "Gabor frames in nite dimensions" (2010), Birkhauser
  14. Terras. A, "Fourier analysis on nite groups and applications" (1999), Cambridge University Press
  15. J. Thomas, "A class of structured frames in nite dimensional hilbert spaces", J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math, 28(4), pp.321~334 (2022)[DOI]

이 간행물의 다른 논문 (13건)

Common fixed point theorems for three mappings in generalized modular metric spacesMaria Joseph John, Sheela Arockiampp. 15-25Generalized crossed modules over generalized group-groupoidsH. Fulya Akızpp. 27-42VC-DIMENSION AND DISTANCE CHAINS IN FdqSteven J. Miller, Justin Cheigh, Alex Iosevich, Ryan Jeong, Xuyan Liu, Brian McDonald, Wyatt Milgrim, Francisco Romero Acosta, Santiago Velazquez Iannuzzelli, Ruben Ascoli, Livia Bettipp. 43-57Applications of fixed point theory in Hilbert spacesKiran Dewanganpp. 59-72Certain subclass of strongly meromorphic close-to-convex functionsGagandeep Singh, Navyodh Singh, Gurcharanjit Singhpp. 73-82
원문 보기