[1] F. Arabyani and A.A. Arefijamaal, Some constructions of K-frames and their duals, Rocky Mt. J. Math., 47(6) (2017),
1749-1764.
[2] D. Baki'{c} and T. Beri'{c}, Finite extensions of Bessel sequences, Banach J. Math. Anal., 9(4) (2015), 1-13.
[3] B.A. Barnes, Majorization, Range inclusion, and factorization for bounded linear operators, Proc. Am. Math. Soc., 133(1)
(2004), 155-162.
[4] J.J. Benedetto and M.W. Frazier, Wavelets, Mathematics and Applications, CRC Press, Inc., Florida, 1994.
[5] H. Bolcskei, F. Hlawatsch and H.G. Feichtinger, Frame-theoretic analyssis of over-sampled filter banks, IEEE Trans.
Signal Process., 46(1) (1998), 3256-3268.
[6] P.G. Casazza and N. Leonhard, Classes of finite equal norm Parseval frames, Contemp. Math., 451(1) (2008), 11-31.
[7] O. Christensen, H.O. Kim and R.Y. Kim, Extensions of Bessel sequences to dual pairs of frames, Appl. Comput. Harmon.
Anal., 34(1) (2013), 224-233.
[8] O. Christensen, An Introduction to Frames and Riesz Bases, Birkh$ddot{a}$user, Boston, 2016.
[9] I. Daubechies, A. Grossmann and Y. Meyer, Painless non-orthogonal expansions, J. Math. Phys., 27(1) (1986),
1271-1283.
[10] I. Deepshikhal and L.K. Vashisht, Extension of Bessel sequences to dual frames in Hilbert spaces, Sci. Bull., Ser. A, Appl.
Math. Phys., 79(2) (2017), 71-82.
[11] R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Am. Math. Soc., 72 (1952), 341-366.
[12] Y.C. Eldar, Sampling with arbitrary sampling and reconstruction spaces and oblique dual frame vectors, J. Fourier.
Anal. Appl., 9(1) (2003), 77-96.
[13] Y.C. Eldar and T. Werther, General framework for consistent sampling in Hilbert spaces, Int. J. Wavelets Multiresolut.
Inf. Process., 3(3) (2005), 347-359.
[14] H.G. Feichtinger and K. Gr$ddot{o}$chenig, A Unified Approach to Atomic Decompositions via Integrable Group
Representations, In: Proc. Conf. Function Spaces and Applications, Lecture Notes in Math., 1302, Springer, Berlin-
Heidelberg-New York, 1988.
[15] P.J.S.G. Ferreira, Mathematics for Multimedia Signal Processing II: Discrete Finite Frames and Signal Reconstruction, In:
Byrnes, J.S. (ed.) Signal processing for multimedia, IOS Press, Amsterdam, 1999.
[16] L. Gu{a}vruc{t}a, Frames for operators, Appl. Comput. Harmon. Anal., 32(1) (2012), 139-144.
[17] K. Gr$ddot{o}$chenig, Describing functions: Atomic decompositions versus frames, Monatsh. Math., 112(1) (1991),
1-42.
[18] D.F. Li and W.C. Sun, Expansion of frames to tight frames, Acta Math. Sin., Engl. Ser., 25 (2009), 287-292.
[19] M. Pawlak and U. Stadtmuller, Recovering band-limited signals under noise, IEEE Trans. Inf. Theory, 42 (1994),
1425-1438.
[20] Zh.Q. Xiang and Y.M. Li, Frame sequences and dual frames for operators, Sci. Asia, 42 (2016), 222-230.
[21] X. Xiao, Y. Zhu and L. Gu{a}vruc{t}a, Some properties of K-frames in Hilbert spaces, Result. Math., 63(3-4) (2013),
1243-1255.
[22] R. Young, An Introduction to Nonharmonic Fourier Series, Academic Press., New York, 1980.
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