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Universität Augsburg
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Universität Augsburg
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Dr. Thiago Carvalho Corso
Universität Stuttgart
spricht am
Donnerstag, 25. April 2024
um
14:30 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| In this talk I will report on improved upper bounds on the optimal constants in the Cwikel-Lieb-Rozenblum (CLR) and Lieb-Thirring (LT) inequalities. More precisely, we explicitly solve a variational problem that has been recently related to upper bounds on these constants in [Invent. Math. 231 (2023), no.1, 111-167.] and [J. Eur. Math. Soc. (JEMS) 23 (2021), no.8, 2583-2600.]. We achieve this through a variational characterization of the L1 norm of the Fourier transform of a function and duality, from which we obtain a reformulation in terms of a variant of the Hadamard three lines lemma. By studying Hardy-like spaces of holomorphic functions in a strip in the complex plane, we are able to provide an analytic formula for the minimizers, and use it to get the best possible upper bounds for the optimal constants in the CLR and LT inequalities achievable by the method of [Invent. Math. 231 (2023), no.1, 111-167. ] and [J. Eur. Math. Soc. (JEMS) 23 (2021), no.8, 2583-2600.]. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Bernd Schmidt |