On the domains of Bessel operators

DOI10.1007/S00023-021-01058-9arXiv2101.01001MaRDI QIDQ6357529

Vladimir Georgescu, Jan Dereziński

Publication date: 4 January 2021

Abstract: We consider the Schr"odinger operator on the halfline with the potential $(m^2-frac14)frac1x^2$, often called the Bessel operator. We assume that $m$ is complex. We study the domains of various closed homogeneous realizations of the Bessel operator. In particular, we prove that the domain of its minimal realization for $|Re(m)|<1$ and of its unique closed realization for $Re(m)>1$ coincide with the minimal second order Sobolev space. On the other hand, if $Re(m)=1$ the minimal second order Sobolev space is a subspace of infinite codimension of the domain of the unique closed Bessel operator. The properties of Bessel operators are compared with the properties of the corresponding bilinear forms.

Mathematics Subject Classification ID

Special quantum systems, such as solvable systems (81Q80) Ordinary differential operators (47E99)

This page was built for publication: On the domains of Bessel operators

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6357529)