Published April 29, 2023
| Published
Journal Article
Open
Sharp inequalities for coherent states and their optimizers
- Creators
-
Frank, Rupert L.
Chicago
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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.
Additional Information
© 2023 the author(s), published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. Partial support through the US National Science Foundation grant DMS-1954995, as well as through the Deutsche Forschungsgemeinschaft (German Research Foundation) through Germany's Excellence Strategy EXC-2111-390814868, is acknowledged.Attached Files
Published - 10.1515_ans-2022-0050.pdf
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10.1515_ans-2022-0050.pdf
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Additional details
- Eprint ID
- 121520
- Resolver ID
- CaltechAUTHORS:20230525-771644200.5
- NSF
- DMS-1954995
- Deutsche Forschungsgemeinschaft (DFG)
- EXC-2111-390814868
- Created
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2023-06-09Created from EPrint's datestamp field
- Updated
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2023-06-09Created from EPrint's last_modified field