"Quantum harmonic analysis on locally compact groups"Halvdansson, SimonA square integrable representation of a locally compact group induces a natural notion of function-operator and operator-operator convolutions. These generalize the convolutions defined in Werner's theory of quantum harmonic analysis on phase space. As a result, we can deduce properties of localization operators, Cohen's class distributions and related objects using a common framework since these can be realized as convolutions. These convolutions have recently been studied in the case where the representation corresponds to time-frequency shifts and time-scale shifts but not in the more general setting of locally compact groups. Apart from setting up the general theory, we also prove that the accumulated scalogram forms an approximate partition of unity, generalizing results on the accumulated spectrogram by Abreu et al to the setting of the affine group. |
| http://univie.ac.at/projektservice-mathematik/e/talks/Halvdansson_2022-02_Strobl_Poster_Abstract_Halvdansson.pdf |
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