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 Schr\"odinger type equations. Indeed, continuity results of both Schr\"odinger 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.

Semi-classical Time-frequency Analysis and Applications

Cordero, Elena;
2017-01-01

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 Schr\"odinger type equations. Indeed, continuity results of both Schr\"odinger 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.
2017
20
4
Art. 26-1
23
http://www.kluweronline.com/issn/1385-0172
https://arxiv.org/abs/1609.00553
Gabor frames; Modulation spaces; Quadratic potentials; Schrödinger equation; Semi-classical analysis; Time-frequency analysis; Mathematical Physics; Geometry and Topology
Cordero, Elena*; de Gosson, Maurice; Nicola, Fabio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1660458
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