Sharp inequalities for coherent states and their optimizers
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 art...
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| Format: | Article |
| Language: | English |
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De Gruyter
2023-04-01
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| Series: | Advanced Nonlinear Studies |
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| Online Access: | https://doi.org/10.1515/ans-2022-0050 |
| _version_ | 1797832477855711232 |
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| author | Frank Rupert L. |
| author_facet | Frank Rupert L. |
| author_sort | Frank Rupert L. |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-09T14:08:31Z |
| format | Article |
| id | doaj.art-30ac36de6af44e86a6f60f675c268cb1 |
| institution | Directory Open Access Journal |
| issn | 2169-0375 |
| language | English |
| last_indexed | 2024-04-09T14:08:31Z |
| publishDate | 2023-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-30ac36de6af44e86a6f60f675c268cb12023-05-06T15:50:45ZengDe GruyterAdvanced Nonlinear Studies2169-03752023-04-0123118522010.1515/ans-2022-0050Sharp inequalities for coherent states and their optimizersFrank Rupert L.0Mathematisches Institut, Ludwig-Maximilans Universität München, Theresienstr. 39, 80333 München, GermanyWe 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.https://doi.org/10.1515/ans-2022-0050functional inequalitiescoherent statesinequalities for analytic functionsrepresentations of lie groupsisoperimetric inequalityprimary 39b62secondary 22e7030h1030h2081r30 |
| spellingShingle | Frank Rupert L. Sharp inequalities for coherent states and their optimizers Advanced Nonlinear Studies functional inequalities coherent states inequalities for analytic functions representations of lie groups isoperimetric inequality primary 39b62 secondary 22e70 30h10 30h20 81r30 |
| title | Sharp inequalities for coherent states and their optimizers |
| title_full | Sharp inequalities for coherent states and their optimizers |
| title_fullStr | Sharp inequalities for coherent states and their optimizers |
| title_full_unstemmed | Sharp inequalities for coherent states and their optimizers |
| title_short | Sharp inequalities for coherent states and their optimizers |
| title_sort | sharp inequalities for coherent states and their optimizers |
| topic | functional inequalities coherent states inequalities for analytic functions representations of lie groups isoperimetric inequality primary 39b62 secondary 22e70 30h10 30h20 81r30 |
| url | https://doi.org/10.1515/ans-2022-0050 |
| work_keys_str_mv | AT frankrupertl sharpinequalitiesforcoherentstatesandtheiroptimizers |