Semi-classical Time-frequency Analysis and Applications

Semi-classical Time-frequency Analysis and Applications 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 ℏ $\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 ℏ $\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 ℏ $\hbar $ . Continuity properties of more general Fourier integral operators (FIOs) and their sparsity are also investigated. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Mathematical Physics, Analysis and Geometry" Springer Journals

Semi-classical Time-frequency Analysis and Applications

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Publisher
Springer Netherlands
Copyright
Copyright © 2017 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Physics; Theoretical, Mathematical and Computational Physics; Analysis; Geometry; Group Theory and Generalizations; Applications of Mathematics
ISSN
1385-0172
eISSN
1572-9656
D.O.I.
10.1007/s11040-017-9259-8
Publisher site
See Article on Publisher Site

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 ℏ $\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 ℏ $\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 ℏ $\hbar $ . Continuity properties of more general Fourier integral operators (FIOs) and their sparsity are also investigated.

Journal

"Mathematical Physics, Analysis and Geometry"Springer Journals

Published: Nov 30, 2017

References

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