Sharp inequalities for coherent states and their optimizers
Abstract: We are interested in sharp functional inequalities for the coherent state transform related to the Wehrl conjecture and its generalizations. This conjecture was settled by Lieb in the case of the Heisenberg group, Lieb and Solovej for SU (2), and Kulikov for SU (1, 1) and the affine group. In this article, we give alternative proofs and characterize, for the first time, the optimizers in the general case. We also extend the recent Faber-Krahn-type inequality for Heisenberg coherent states, due to Nicola and Tilli, to the SU (2) and SU (1, 1) cases. Finally, we prove a family of reverse Hölder inequalities for polynomials, conjectured by Bodmann.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Sharp inequalities for coherent states and their optimizers ; volume:23 ; number:1 ; year:2023 ; extent:28
Advanced nonlinear studies ; 23, Heft 1 (2023) (gesamt 28)
- Creator
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Frank, Rupert L.
- DOI
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10.1515/ans-2022-0050
- URN
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urn:nbn:de:101:1-2023042914304326862212
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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14.08.2025, 10:49 AM CEST
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Associated
- Frank, Rupert L.
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