Imaginary powers of a Laguerre differential operator
Let \(\mathcal{L}_\alpha\) be a self-adjoint extension of the Laguerre differential operator \[ L_\alpha=-\Delta+| x| ^2+\sum_{i=1}^{d} \frac{1}{x_i^2}\Big(\alpha_i^2-\frac{1}{4} \Big), \qquad \alpha_i\in \{-\frac{1}{2}\}\cup [\frac{1}{2},\infty). \] It is proved that \(\mathcal{L}_\alpha^{-i\gamma}\) \((\gamma\in \mathbb{R})\) is a Calderon-Zygmund operator, which implies some results by the general theory.
imaginary power of a Laguerre differential operator
scientific article; zbMATH DE number 5848544