Localization operators on the Euclidean motion group on the plane

Abstract

In this work, we compute a bounded linear operator that localizes functions parametrized by translations and rotations. Such operators are called localization operators and are important in signal analysis, image analysis, quantum mechanics and pseudo-differential operators. Functions parametrized by translations and rotations may be considered as functions on the Euclidean motion group, for which no standard construction of coherent states is possible. Coherent states are the crucial ingredient in phase space localization and these will be constructed using the regular representation on the Euclidean motion group on the plane and an appropriate admissible wavelet on the plane.