Analytic Differential Operators on the Unit Disk

2018/06/11 by Robert Carlson, Carlson, Robert
Mathematics · #34L05 #34M03 #47B25 #47E05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:34L05 #msc:34M03 #msc:47B25 #msc:47E05

paper · pdf · doi:10.48550/arxiv.1806.04250

arxiv created 2019/01/21 · arxiv updated 2019/01/23

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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