Fractional operators as traces of operator-valued curves

Roberta Musina; Alexander I. Nazarov

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arXiv · 2208.06873

Fractional operators as traces of operator-valued curves

Roberta Musina·Alexander I. Nazarov

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Abstract

We relate non integer powers ${\mathcal L}^{s}$, $s>0$ of a given (unbounded) positive self-adjoint operator $\mathcal L$ in a real separable Hilbert space $\mathcal H$ with a certain differential operator of order $2\lceil{s}\rceil$, acting on even curves $\mathbb R\to \mathcal H$. This extends the results by Caffarelli--Silvestre and Stinga--Torrea regarding the characterization of fractional powers of differential operators via an extension problem.

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Roberta Musina, Alexander I. Nazarov. 2022-08-14. Fractional operators as traces of operator-valued curves. https://arxiv.org/abs/2208.06873

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