论文标题
分数操作员作为操作员值曲线的痕迹
Fractional operators as traces of operator-valued curves
论文作者
论文摘要
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 $。这扩展了Caffarelli-silvestre和stinga--torrea关于通过扩展问题对差分运算符的分数幂的表征的结果。
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.
