Fractional operators as traces of operator-valued curves

DOI10.1016/J.JFA.2024.110443arXiv2208.06873OpenAlexW4394769843MaRDI QIDQ6407821

A. I. Nazarov, Roberta Musina

Publication date: 14 August 2022

Abstract: We relate non integer powers ${mathcalL}^s$, $s>0$ of a given (unbounded) positive self-adjoint operator $mathcalL$ in a real separable Hilbert space $mathcalH$ with a certain differential operator of order $2lceilsceil$, acting on even curves $mathbbRomathcalH$. This extends the results by Caffarelli--Silvestre and Stinga--Torrea regarding the characterization of fractional powers of differential operators via an extension problem.

Full work available at URL: https://doi.org/10.1016/j.jfa.2024.110443

Mathematics Subject Classification ID

Spaces of vector- and operator-valued functions (46E40) Linear differential equations in abstract spaces (34G10) Fractional partial differential equations (35R11)

Related Items (1)

A survey of results of St. Petersburg State university research school on nonlinear partial differential equations. I

This page was built for publication: Fractional operators as traces of operator-valued curves

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6407821)