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-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. 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. Continuity properties of more general Fourier integral operators (FIOs) and their sparsity are also investigated.
Semi-classical Time-frequency Analysis and Applications / Cordero, Elena; de Gosson, Maurice; Nicola, Fabio. - In: MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY. - ISSN 1385-0172. - STAMPA. - 20:4(2017).
|Titolo:||Semi-classical Time-frequency Analysis and Applications|
|Data di pubblicazione:||2017|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1007/s11040-017-9259-8|
|Appare nelle tipologie:||1.1 Articolo in rivista|
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