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arXiv · 1609.00553

Semi-classical Time-frequency Analysis and Applications

Elena Cordero·Maurice de Gosson·Fabio Nicola
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Abstract

This work represents a first systematic attempt to create a common ground for semi-classical and time-frequency analysis. These two different areas combined together provide interesting outcomes in terms of Schrödinger type equations. Indeed, continuity results of both Schrödinger propagators and their asymptotic solutions are obtained on $\hbar$-dependent Banach spaces, the semi-classical version of the well-known modulation spaces. Moreover, their operator norm is controlled by a constant independent of the Planck's constant $\hbar$. The main tool in our investigation is the joint application of standard approximation techniques from semi-classical analysis and a generalized version of Gabor frames, dependent of the parameter $\hbar$. Continuity properties of more general Fourier integral operators (FIOs) and their sparsity are also investigated.

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Elena Cordero, Maurice de Gosson, Fabio Nicola. 2016-09-22. Semi-classical Time-frequency Analysis and Applications. https://doi.org/10.1007/s11040-017-9259-8

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