논문KCI 등재
Gabor frames in l²(R) from Gabor frames in l²(R)
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In this paper we discuss about the image of Gabor frame under a unitary operator and derive a sufficient condition under which a unitary operator from $L^2 (\mathbb R)$ to $l^2 (\mathbb Z)$ maps Gabor frame in $L^2 (\mathbb R)$ to a Gabor frame in $l^2 (\mathbb Z)$.
Abstract
In this paper we discuss about the image of Gabor frame under a unitary operator and derive a sufficient condition under which a unitary operator from $L^2 (\mathbb R)$ to $l^2 (\mathbb Z)$ maps Gabor frame in $L^2 (\mathbb R)$ to a Gabor frame in $l^2 (\mathbb Z)$.
참고문헌 (16)
- Z. Amiri, "Bessel subfusion sequences and subfusion frames", Iran. J. Math. Sci. Inform, 8(1), pp.31~38 (2013)
- P. G. Cazassa, "Frames of subspaces. Wavelets, frames and operator theory", Contemp. Math, 345, pp.87~113 (2004), Amer. Math. Soc.
- P. G. Cazassa, "Finite Frames Theory and Applications, Applied and Numerical Harmonic Analysis series" (2013)
- O. Christensen, "An Introduction to Frames and Riesz Bases" (2016), Birkhauser
- O. Christensen, "Oblique dual frames and shift-invariant spaces", Appl. Comput. Harmon. Anal, 17, pp.48~68 (2004)
- I. Daubechies, "Painless nonorthogonal expansions", J. Math. Physics, 27, pp.1271~1283 (1986)
- R. J. Duffin, "A class of non-harmonic Fourier series", Trans. Amer. Math. Soc, 72, pp.341~366 (1952)
- T. C. Easwaran Nambudiri, "Characterization of WeylHeisenberg frame operators", Bull.Sci. Math, 137, pp.322~324 (2013)
- T. C. Easwaran Nambudiri, "Generalised Weyl-Heisenberg frame operators", Bull.Sci. Math, 136, pp.44~53 (2012)
- Feichtinger H. G, "Gabor Analysis and Algorithms: Theory and Applications" (1998), Birkhauser
- D. Gabor, "Theory of communication", J.IEEE, 93, pp.429~457 (1946)
- Gotz E.Pfander, "Gabor frames in finite dimensions" (2010), Birkhauser
- K. Grochenig, "Foundations of Time Frequency Analysis" (2001), Birkhauser
- A. J. E. M. Janssen, "Gabor representation of generalized functions", J. Math. Anal. Appl, 83, pp.377~394 (1981)
- A. J. E. M. Janssen, "From continuous to discrete Weyl-Heisenberg frames through sampling", J. Four. Anal. Appl, 3(5), pp.583~596 (1971)
- S. Li, "Pseudoframes for subspaces with applications", J. Fourier Anal. Appl, 10, pp.409~431 (2004)
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