Characterization of essential sets (Q1396370)

The authors study essential sets for a Kato measure in \((\mathbb{R}^{d}\setminus\{0\})\), \(d\geq 2\). Using the characterization of the Picard principle via the Green kernel associated to the Schrödinger operator \(\Delta-\mu\), they give a new characterization of such sets when \(\mu=(f(\cdot)/\| \cdot\| )^2\lambda\), where \(f\) is assumed to be rotation free nonnegative, decreasing and locally Hölder continuous on \(\{0<\| x\| \leq 1\}\). In particular a result given by \textit{T. Tada} [Kodai Math. J. 14, 134--143 (1991; Zbl 0731.30034)] is obtained in the case when \(d=2\) and \(f(r)=-\log r\).