Time–Frequency analysis of localization operators

Localization operators on homogeneous spaces

Let $G$ be a locally compact group, $H$ be a compact subgroup of $G$ and $varpi$ be a representation of the homogeneous space $G/H$ on a Hilbert space $mathcal H$. For $psi in L^p(G/H), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $L_{psi,zeta} $ on $mathcal H$ and we show that it is a bounded operator. Moreover, we prove that the localizat...

Multiscale Analysis and Localization of Random Operators

A discussion of the method of multiscale analysis in the study of localization of random operators based on lectures given at Random Schrödinger operators: methods, results, and perspectives, États de la recherche, Université Paris 13, June 2002

Time - Frequency Analysis of Localization Operators

localization operators on homogeneous spaces

let $g$ be a locally compact group, $h$ be a compact subgroup of $g$ and $varpi$ be a representation of the homogeneous space $g/h$ on a hilbert space $mathcal h$. for $psi in l^p(g/h), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $l_{psi,zeta} $ on $mathcal h$ and we show that it is a bounded operator. moreover, we prove that the localizat...

Localization Operators via Time-Frequency Analysis

A systematic overview of localization operators using a time-frequency approach is given. Sufficient and necessary regularity results for localization operators with symbols and windows living in various function spaces (such as L or modulation spaces) are discussed. Finally, an exact and an asymptotic product formulae are presented.