Some results of K-frames and their multipliers

K -frames are strong tools for the reconstruction of elements from range of a bounded linear operator K on a separable 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.

Keywords:

K -frame, K -dual, K -left inverse K -right inverse, multiplier,

PDF

___

[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, Grossmann A, Meyer Y. Painless nonorthogonal expansions. Journal of Mathematical Physics 1986; 27: 1271-1283.
[19] Găvruţa L. Frames for operators. Applied and Computational Harmonic Analysis 2012; 32: 139-144.
[20] Ismayilov MI, Nasibov YI. One generalization of Banach frame. Azerbaijan Journal of Mathematics 2016; 6 (2): 143-159.
[21] Rahimi A, Balazs P. Multipliers for p- Bessel sequence in Banach spaces. Integral equations Operator Theory 2010; 68: 193-205.
[22] Shamsabadi M, Arefijamaal A. The invertibility of fusion frame multipliers. Linear and Multilinear Algebra 2016; 65 (5): 1062-1072.
[23] Stoeva DT, Balazs P. Invertibility of multipliers. Applied and Computational Harmonic Analysis 2012; 33 (2): 292-299.
24] Majdak P, Balazs P, Kreuzer W, Do¨rfler M. A time-frequency method for increasing the signal-to-noise ratio in system identification with exponential sweeps. In: Proceedings of the 36th IEEE international Conference on Acoustics, Speech and Signal Processing, ICASSP; 2011. pp. 3812-3815.
[25] Xiao XC, Zhu YC, Găvruţa L. Some properties of K-frames in Hilbert spaces. Results in Mathematics 2013; 63: 1243-1255.