Analytic Differential Operators on the Unit Disk
Classical Analysis and ODEs
2019-01-23 v2
Abstract
Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical Riemann and Heun equations. Symmetric minimal operators are characterized. A regular class whose leading coefficients have no zeros on the unit circle are shown to be essentially self-adjoint. Eigenvalue asymptotics are established. Some extensions to non-self-adjoint operators are also considered.
Cite
@article{arxiv.1806.04250,
title = {Analytic Differential Operators on the Unit Disk},
author = {Robert Carlson},
journal= {arXiv preprint arXiv:1806.04250},
year = {2019}
}