• Korean Journal of Mathematics
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• v.28 no.4
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• pp.877-888
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• 2020

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 L²(ℝ) to 𝑙²(ℤ) maps Gabor frame in L²(ℝ) to a Gabor frame in 𝑙²(ℤ).

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.321-334
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• 2022

We introduce a special class of structured frames having single generators in finite dimensional Hilbert spaces. We call them as pseudo B-Gabor like frames and present a characterisation of the frame operators associated with these frames. The concept of Gabor semi-frames is also introduced and some significant properties of the associated semi-frame operators are discussed.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.315-328
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• 2021

A characterization of frame operators of finite Gabor frames is presented here. Regularity aspects of Gabor frames in 𝑙²(ℤ_N) are discussed by introducing associated semi-frame operators. Gabor type frames in finite dimensional Hilbert spaces are also introduced and discussed.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1841-1846
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• 2013

In this paper we establish some new results on sums of Hilbert space frames and Riesz bases. We also provide a correction to some recently established results in [2].

• Journal of the Korean Physical Society
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• v.73 no.9
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• pp.1269-1278
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• 2018

Using the thawed Gaussian wave packets [E. J. Heller, J. Chem. Phys. 62, 1544 (1975)] and the adaptive reinitialization technique employing the frame operator [L. M. Andersson et al., J. Phys. A: Math. Gen. 35, 7787 (2002)], a trajectory-based Gaussian wave packet method is introduced that can be applied to scattering and time-dependent problems. This method does not require either the numerical multidimensional integrals for potential operators or the inversion of nearly-singular matrices representing the overlap of overcomplete Gaussian basis functions. We demonstrate a possibility that the method can be a promising candidate for the time-dependent $Schr{\ddot{o}}dinger$ equation solver by applying to tunneling, high-order harmonic generation, and above-threshold ionization problems in one-dimensional model systems. Although the efficiency of the method is confirmed in one-dimensional systems, it can be easily extended to higher dimensional systems.