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math.FA2026
A counterexample to the Kato conjecture for positive commutators
Rupert L. Frank, Paata Ivanisvili
We disprove the conjectural converse to Kato's positivity criterion for commutators of functions of the canonical position and momentum operators and by showing that the op…
math.FA2026
The sharp extension norm for a planar sector
Rupert L. Frank, Paata Ivanisvili
We compute explicitly the infimum of the norms of -extension operators for planar sectors and exhibit an extension operator attaining this infimum. This solves an open pro…
math.FA2026
Sobolev extensions, interpolation inequalities and consequences
Rupert L. Frank, Pekka Koskela, Riddhi Mishra
We prove Sobolev interpolation inequalities on extension domains that have a form reminiscent of the corresponding whole-space inequalities. This form is crucial in certain applica…