Journals / Turkish Journal of Mathematics / 2020 / Cilt: 44 - Sayı: 2

Some results of K− frames and their multipliers

Pages
538–552
Publication Date
2022-11-05
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In this paper, we study some properties of K -frames and introduce the K -frame multipliers.We also focus on representing elements from the range of K by K -frame multipliers.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:K -frames are strong tools for the reconstruction of elements from range of a bounded linear operator K on aseparable Hilbert space H.
📊
Key Findings & Data:K -frames are strong tools for the reconstruction of elements from range of a bounded linear operator K on aseparable Hilbert space H.
💡
Conclusion & Impact:In this paper, we study some properties of K -frames and introduce the K -frame multipliers.We also focus on representing elements from the range of K by K -frame multipliers.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

K -frames are strong tools for the reconstruction of elements from range of a bounded linear operator K on aseparable Hilbert space H. In this paper, we study some properties of K -frames and introduce the K -frame multipliers.We also focus on representing elements from the range of K by K -frame multipliers.

🔖

Cite This Article

AREFIJAMAAL, A. A., SHAMSABADI, M. (2022). Some results of K− frames and their multipliers. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 2, 538–552. https://ajindex.com/articles/607566

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (18)

  1. Arabyani Neyshaburi F, Arefijamaal A. Some construction of K -frames and their duals. The Rocky Mountain Journal of Mathematics 2017; 1 (6): 1749-1764
  2. Arefijamaal A, Zekaee E. Signal processing by alternate dual Gabor frames. Applied and Computational Harmonic Analysis 2013; 35: 535-540
  3. Arefijamaal A, Zekaee E. Image processing by alternate dual Gabor frames. Bulletin of the Iranian Mathematical Society 2016; 42 (6): 1305-1314
  4. Balazs P. Basic definition and properties of Bessel multipliers. Journal of Mathematical Analysis and Applications 2007: 325 (1): 571-585
  5. Balazs P. Bayer D, Rahimi A. Multipliers for continuous frames in Hilbert spaces. Journal of Physics. A 2012; 45 (24): 244023, 20 pp
  6. Balazs P, Laback B, Eckel G, Deutsch WA. Time-frequency sparsity by removing perceptually irrelevant components using a simple model of simultaneous masking. IEEE Trans. Audio Speech Lang. Processing 2010; 18 (1): 34-49
  7. Balazs P, Shamsabadi M, Arefijamaal A, Rahimi A. U -cross Gram matrices and their invertibility. Journal of Mathematical Analysis and Applications 2019; 476 (2): 367-390
  8. Balazs P, Stoeva DT. Representation of the inverse of a frame multiplier. Journal of Mathematical Analysis and Applications 2015; 422: 981-994
  9. Bilalov BT, Ismailov MI, Nasibov YI. Uncountable frames in non-separable Hilbert spaces and their characterization. Azerbaijan Journal of Mathematics 2018; 8 (1): 151-178
  10. Bilalov BT, Guliyeva FA. Noetherian perturbation of frames. Pensee Journal 2013; 75 (12): 425-431
  11. Bilalov BT, Guliyeva FA. t-frames and their Noetherian perturbation. Complex Analysis and Operator Theory 2014; 8 (7): 1405-1418
  12. Bodmannand BG, Paulsen VI. Frames, graphs and erasures. Linear Algebra and its Applications 2005; 404: 118-146
  13. Bolcskel H, Hlawatsch F, Feichtinger HG. Frame-theoretic analysis of oversampled filter banks. IEEE Transactions on Signal Processing 1998; 46: 3256-3268
  14. Casazza PG. The art of frame theory. Taiwanese Journal of Mathematics 2000; 4 (2): 129-202
  15. Christensen O. A short introduction to frames, Gabor systems, and wavelet systems. Azerbaijan Journal of Mathematics 2014; 4 (1): 25-39
  16. Christensen O. Frames and Bases: An Introductory Course. Birkhäuser, Boston. 2008
  17. Christensen O, Zakowicz MI. Paley-Wiener type perturbations of frames and the deviation from the perfect reconstruction. Azerbaijan Journal of Mathematics 2017; 7 (1): 59-69
  18. Dubechies I, Grossman