LOCALIZATION OPERATORS AND TIME-FREQUENCY ANALYSIS

Localization operators have been object of study in quantum mechanics, in PDE and signal analysis recently. In engineering, a natural language is given by time-frequency analysis. Arguing from this point of view, we shall present the theory of these operators developed so far. Namely, regularity properties, composition formulae and their multilinear extension shall be highlighted. Time-frequency analysis will provide tools, techniques and function spaces. In particular, we shall use modulation spaces, which allow “optimal” results in terms of regularity properties for localization operators acting on L²(ℝ^d).