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arXiv · 1308.2640

Gabor Frame Decomposition of Evolution Operators and Applications

Michele Berra
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Abstract

We compute the Gabor matrix for Schrödinger-type evolution operators. Precisely, we analyze the Heat Equation, already presented in \cite{2012arXiv1209.0945C}, 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. This work is the natural prosecution of the ideas presented in \cite{2012arXiv1209.0945C} and \cite{MR2502369}.

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Michele Berra. 2014-02-25. Gabor Frame Decomposition of Evolution Operators and Applications. https://doi.org/10.1007/s11868-014-0090-8

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