On the Schrödinger operator based on the fractional Laplacian (Q2770183)

The authors announce results on the potential theory associated to a symmetric \(\alpha\)-stable Lévy process in \(\mathbb{R}^{d}\). In particular, they study existence and properties of \(q\)-harmonic functions, for functions \(q\) belonging to the so-called Kato class of index \(\alpha\in(0,2)\). The authors study weakly \(q\)-harmonic functions, defined by the condition NEWLINE\[NEWLINE {\widetilde{\Delta}}^{\alpha/2}u+qu=0 NEWLINE\]NEWLINE (in the sense of distributions), where \({\widetilde{\Delta}}^{\alpha/2}\) is the operator defined in their previous work [Studia Math. 133, No.~1, 53-92 (1999; Zbl 0923.31003)].