We compute the Gabor matrix for Schrödinger-type evolution operators. Precisely, we analyze the Heat Equation giving the exact expression of the Gabor matrix which leads to better numerical evaluations. Then, using asymptotic integration techniques, we obtain an upper bound for the Gabor matrix in one-dimension for the generalized Heat Equation, new in the literature. Using Maple software, we show numeric representations of the coefficients’ decay. Finally, we show the super-exponential decay of the coefficients of the Gabor matrix for the Harmonic Repulsor, together with some numerical evaluations.

Gabor frame decomposition of evolution operators and applications

BERRA, MICHELE
2014

Abstract

We compute the Gabor matrix for Schrödinger-type evolution operators. Precisely, we analyze the Heat Equation giving the exact expression of the Gabor matrix which leads to better numerical evaluations. Then, using asymptotic integration techniques, we obtain an upper bound for the Gabor matrix in one-dimension for the generalized Heat Equation, new in the literature. Using Maple software, we show numeric representations of the coefficients’ decay. Finally, we show the super-exponential decay of the coefficients of the Gabor matrix for the Harmonic Repulsor, together with some numerical evaluations.
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http://arxiv.org/pdf/1308.2640
http://link.springer.com/article/10.1007/s11868-014-0090-8?sa_campaign=email/event/articleAuthor/onlineFirst
Gabor frames; evolution equations; Time frequency analysis
M. Berra
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/143236
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