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Sharpening lower bound in some inequalities for frames in Hilbert spaces

Mohsen Erfanian Omidvar|Fahimeh Sultanzadeh|Mahmood Hassani|Rajab Ali Kamyabi Gol
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2021.12|한국수학논문집 (Korean Journal of Mathematics)|제29권 제4호|pp. 725-732

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참고문헌

키워드

FrameHilbert spaceParseval frame
주제분류수학

초록

This paper aims to present a new lower bound for some inequalities related to Frames in Hilbert space. Some refinements of the inequalities for general frames and alternate dual frames under suitable conditions are given. These results refine the remarkable results obtained by Balan et al. and Gavruta.

Abstract

This paper aims to present a new lower bound for some inequalities related to Frames in Hilbert space. Some refinements of the inequalities for general frames and alternate dual frames under suitable conditions are given. These results refine the remarkable results obtained by Balan et al. and Gavruta.

참고문헌 (13)

  1. R. Balan, "A new identity for Parseval frames", Proc. Amer. Math. Soc, 135, pp.1007~1015 (2007)
  2. P. G. Casazza, "The art of frame theory", Taiwanese J. Math, 4, pp.129~201 (2000)
  3. P. G. Casazza, "Frames of subspaces , Wavelets, frames and operator theory", Con-temp. Math, 345, pp.87~113 (2004)
  4. O. Christensen, "An introduction to frames and Riesz bases" (2016), springer
  5. I. Daubechies, "Ten Lectures on Wavelets" (1992), SIAM
  6. J. Du_n, "A class of nonharmonic Fiurier series", Trans. Amer. Math. Soc, 72, pp.341~366 (1952)
  7. Y. C. Eldar, "Optimal tight frames and quantum measurement", IEEE Trans. Inform. Theory, 48, pp.599~610 (2002)
  8. L. Gavruta, "Frames for operators", Appl Comput Harmon Anal, 32, pp.139~144 (2012)
  9. P. Gavruta, "On some identities and inequalities for frames in Hilbert spaces", J. Math. Anal. Appl, 321, pp.469~478 (2006)
  10. Q.P. Guo, "Some equalities and inequalities for fusion frames", Springer Plus, 5, pp.10~ (2016)
  11. D. Han, "Frames, bases and group representations", Mem. Amer. Math. Soc, 147, pp.94~ (2000)
  12. R. Vale, "Tight frames and their symmetries", Constr. Approx, 21, pp.83~112 (2005)
  13. L. Zou, "Improved arithmetic-geometric mean inequality and its application", J. Math. Inequal, 9, pp.107~111 (2015)

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