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Linear and Multilinear Algebra Volume 71, 2023 - Issue 2
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Research Article

Averaged numerically optimal dual frames for erasures

Deepshikhaa Department of Mathematics, Shyampur Siddheswari Mahavidyalaya, University of Calcutta, Howrah, IndiaCorrespondence[email protected]
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Aniruddha Samantab Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, IndiaORCID Iconhttps://orcid.org/0000-0003-2836-8504View further author information
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Pages 301-316 | Received 04 May 2021, Accepted 09 Jan 2022, Published online: 02 Feb 2022

References

  • Duffin RJ, Schaeffer AC. A class of nonharmonic Fourier series. Trans Am Math Soc. 1952;72:341–366.
  • Daubechies I, Grossmann A, Meyer Y. Painless nonorthogonal expansions. J Math Phys. 1986;27:1271–1283.
  • Casazza PG, Kovačević J. Equal-norm tight frames with erasures. Adv Comput Math. 2003;18:387–430.
  • Goyal V, Kovačević J, Kelner J. Quantized frame expansions with erasures. Appl Comput Harmon Anal. 2001;10:203–233.
  • Strohmer T, Heath RW. Grassmannian frames with applications to coding and communication. Appl Comput Harmon Anal. 2003;14(3):257–275.
  • Holmes R, Paulsen V. Optimal frames for erasures. Linear Algebra Appl. 2004;377:31–51.
  • Lopez J, Han D. Optimal dual frames for erasures. Linear Algebra Appl. 2010;432(1):471–482.
  • Leng J, Han D. Optimal dual frames for erasures II. Linear Algebra Appl. 2011;435(6):1464–1472.
  • Pehlivan S, Han D, Mohapatra R. Linearly connected sequences and spectrally optimal dual frames for erasures. J Funct Anal. 2013;265(11):2855–2876.
  • Arabyani-Neyshaburi F, Arefijamaal AA, Sadeghi G. Numerically and spectrally optimal dual frames in Hilbert spaces. Linear Algebra Appl. 2020;604:52–71.
  • Christensen O. An introduction to frames and Riesz bases. 2nd ed. Berlin: Birkhäuser; 2016.
  • Benedetto J, Li S. The theory of multiresolution analysis frames and applications to filter banks. Appl Comput Harmon Anal. 1998;5:389–427.
  • Bodmann BG, Paulsen VI. Frames, graphs and erasures. Linear Algebra Appl. 2005;404:118–146.
  • Bodmann BG, Paulsen VI. Frame paths and error bounds for sigma-delta quantization. Appl Comput Harmon Anal. 2007;22(2):176–197.
  • Casazza PG. The art of frame theory. Taiwan J Math. 2000;4(2):129–202.
  • Casazza PG, Kutyniok G. Finite frames: theory and applications. Berlin: Birkhäuser; 2012.
  • Christensen O, Deng B, Heil C. Density of Gabor frames. Appl Comput Harmon Anal. 1999;7:292–304.
  • Chien MT, Gau HL, Li CK, et al. Product of operators and numerical range. Linear Multilinear Algebra. 2016;64(1):58–67.
  • Deepshikha, Vashisht LK. A note on discrete frames of translates in CN. TWMS J Appl Eng Math. 2016;6(1):143–149.

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