391 citations · 1.8k across the 147 of their papers we have counts for
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Sharp inequalities for coherent states and their optimizers
Rupert L. Frank
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…
Asymptotics of singular values for quantum derivatives
Rupert L. Frank, Fedor Sukochev, Dmitriy Zanin
We obtain Weyl type asymptotics for the quantised derivative $\dbar f$ of a function from the homgeneous Sobolev space on The asympt…
Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence
Jean Dolbeault, Maria J. Esteban, Alessio Figalli +2
We prove a sharp quantitative version for the stability of the Sobolev inequality with explicit constants. Moreover, the constants have the correct behavior in the limit of large d…
Rearrangement methods in the work of Elliott Lieb
Rupert L. Frank
We review some topics in the theory of symmetric decreasing rearrangements with a particular focus on Lieb's fundamental contributions. Topics covered include the Brascamp--Lieb--L…
The work of Elliott Lieb
Rupert L. Frank
On the occasion of Elliott Lieb being awarded the Gauss Prize 2022, we give a non-technical overview over some of his seminal works in mathematical physics. We emphasize, in partic…
The Scott conjecture for large Coulomb systems: a review
Rupert L. Frank, Konstantin Merz, Heinz Siedentop
We review some older and more recent results concerning the energy and particle distribution in ground states of heavy Coulomb systems. The reviewed results are asymptotic in natur…