Quantum harmonic analysis on locally compact groups
Simon Halvdansson
Abstract
On a locally compact group we introduce covariant quantization schemes and analogs of phase space representations as well as mixed-state localization operators. These generalize corresponding notions for the affine group and the Heisenberg group. The approach is based on associating to a square integrable representation of the locally compact group two types of convolutions between integrable functions and trace-class operators. In the case of non-unimodular groups these convolutions only are well-defined for admissible operators, which is an extension of the notion of admissible wavelets as has been pointed out recently in the case of the affine group.
Topics & Concepts
MathematicsSquare-integrable functionUnimodular matrixNoncommutative harmonic analysisLocally compact spaceLocally compact groupCovariant transformationPure mathematicsIntegrable systemCompact operator on Hilbert spaceAffine transformationHeisenberg groupLie groupAlgebra over a fieldCompact operatorExtension (predicate logic)Mathematical physicsComputer scienceProgramming languageMathematical Analysis and Transform MethodsSeismic Imaging and Inversion TechniquesMedical Imaging Techniques and Applications