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A Class of Structured Frames in Finite Dimensional Hilbert Spaces

Jineesh Thomas|N. M. Madhavan Namboothiri|T. C. Easwaran Nambudiri
한국수학교육학회|2022.11|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제29권 제4호|pp. 321-334

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참고문헌

키워드

Gabor frame operatorGabor framemixed frame operatorsemi-frame operator.
주제분류수학

초록

We introduce a special class of structured frames having single generators in fi nite 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 signi ficant properties of the associated semi-frame operators are discussed.

Abstract

We introduce a special class of structured frames having single generators in fi nite 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 signi ficant properties of the associated semi-frame operators are discussed.

참고문헌 (13)

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  4. R.J. Duffin, "A class of non-harmonic Fourier series", Trans. Amer. Math. Soc, 72, pp.341~366 (1952)
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  8. K. Gröchenig, "Foundations of Time Frequency Analysis" (2001), Birkhäuser
  9. D. Han, "Frames, Bases and Group representations", Mem. Am. Math. Soc, 147, pp.697~714 (2000)
  10. M. Janssen, "Gabor representation of generalized functions", J. Math. Anal. Appl, 83, pp.377~394 (1981)
  11. J. Laurence, "Linear independence of Gabor systems in finite dimensional vector spaces", J. Fourier Anal. Appl, 11, pp.715~726 (2005)
  12. R. D. Malikiosis, "A note on Gabor frames in finite dimensions", Appl. Comp. Harmonic Anal, 38, pp.318~330 (2015)
  13. N. M. Madhavan Namboothiri, "Frame Operators and Semi-frame Operators of Finite Gabor Frames", 순수 및 응용수학, 28(4), pp.315~328 (2021), 한국수학교육학회[DOI]

관련 논문AI추천

Frame Operators and Semi-frame Operators of Finite Gabor FramesJineesh Thomas, N. M. Madhavan Namboothiri, T. C. Easwaran Nambudiri한국수학교육학회 · 이론수학과 교직수학2021 · 제28권 제4호Gabor Like Structured Frames in Separable Hilbert SpacesJineesh Thomas, N.M.M. Namboothiri, T.C.E. Nambudiri한국수학교육학회 · 이론수학과 교직수학2024 · 제31권 제2호Gabor frames in l²(R) from Gabor frames in l²(R)Eldo Varghese, Jineesh Thomas, Madhavan Namboothiri N M강원경기수학회 · 한국수학논문집2020 · 제28권 제4호G-frames as Sums of Some g-orthonormal BasesAbbas Najati, Mohammad Reza Abdollahpour경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2013 · 제53권 제1호Generalized pseudo $B$-Gabor frames on finite abelian groupsJineesh Thomas, Madhavan Namboothiri N M강원경기수학회 · 한국수학논문집2024 · 제32권 제1호Ultra g-Bessel Sequences in Hilbert SpacesAbbas Najati, Mohammad Reza Abdollahpour경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제1호

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