Fractional operators as traces of operator-valued curves

Fractional operators as traces of operator-valued curves

We relate non integer powers Ls, s>0 of a given (unbounded) positive self-adjoint operator L in a real separable Hilbert space H with a certain differential operator of order 2⌈s⌉, acting on even curves R→H. This extends the results by Caffarelli–Silvestre and Stinga–Torrea regarding the characte...

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Veröffentlicht in:Journal of functional analysis 2024-07, Vol.287 (2), p.110443, Article 110443
Hauptverfasser: Musina, Roberta, Nazarov, Alexander I.
Format: Artikel
Sprache:eng
Schlagworte:
Higher order fractional operators
Operator-valued functions
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Zusammenfassung:We relate non integer powers Ls, s>0 of a given (unbounded) positive self-adjoint operator L in a real separable Hilbert space H with a certain differential operator of order 2⌈s⌉, acting on even curves R→H. This extends the results by Caffarelli–Silvestre and Stinga–Torrea regarding the characterization of fractional powers of differential operators via an extension problem.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2024.110443