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Localization property and Frames II

하영화|류주연
대한수학회 (The Korean Mathematical Society)|2006.01|대한수학회논문집 (Communications of the KMS)|제21권 제1호|pp. 101-115

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Abstract

Localization of sequences with respect to Riesz bases for Hilbert spaces are comparable with perturbation of Riesz bases or frames. Gr$\rm\ddot{o}$chenig first introduced the notion of localization. We introduce more general definition of localization and show that exponentially localized sequences and polynomially localized sequences with respect to Riesz bases are Bessel sequences. Furthermore, they are frames provided some additional conditions are satisfied.

참고문헌 (11)

  1. "Approximation of theinverse frame opertor and applications to Gabor frames", pp.338~ (2000)
  2. "An introduction to frames and Riesz basis" (2003)
  3. "A Paley-Wiener theorem for frames", pp.2199~ (1995)
  4. "Frame perturbations", pp.1217~ (1995)
  5. "Localization of frames II", pp.29~ (2004)
  6. "Ten Lectures on Wavelets" (1992)
  7. "Localization of frames and the invertiblility of the frame operator", pp.105~ (2004)
  8. "Localized frames are finite unions of Rieszsequences", pp.149~ (2003)
  9. "Foundations of time-frequency analysis" (2001)
  10. "Localization property and frames", pp.233~ (2005)
  11. "\it An Introduction to Nonharmonic Fourier Series}" (1980), Academic Press

관련 논문AI추천

On stability of Banach framesLalit Kumar Vashisht, Pawan Kumar Jain, Shiv Kumar Kaushik대한수학회 · 대한수학회보2007 · 제44권 제1호Perturbation of wavelet frames and Riesz bases IJin Lee, Young-Hwa Ha대한수학회 · 대한수학회논문집2004 · 제19권 제1호More on sums of Hilbert space framesA. Najati, E. Osgooei, M. M. Saem, M. R. Abdollahpour대한수학회 · 대한수학회보2013 · 제50권 제6호Cauchy Completeness of κ-framesM. Mahmoudi, M. M. Ebrahimi, M. Vojdani Tabatabaee경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2004 · 제44권 제4호κ-Compact FramesNIZAR MARCUS경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2002 · 제42권 제1호Frame Operators and Semi-frame Operators of Finite Gabor FramesJineesh Thomas, N. M. Madhavan Namboothiri, T. C. Easwaran Nambudiri한국수학교육학회 · 이론수학과 교직수학2021 · 제28권 제4호

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