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arXiv · 1806.04250

Analytic Differential Operators on the Unit Disk

Robert Carlson
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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.

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Robert Carlson. 2018-06-11. Analytic Differential Operators on the Unit Disk. https://arxiv.org/abs/1806.04250

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