Analytic Differential Operators on the Unit Disk

  • Robert CarlsonEmail author


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.


Analytic differential operators Weighted Hardy space Self-adjoint differential operators 

Mathematics Subject Classification

47E05 47B25 34L05 34M03 



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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Colorado at Colorado SpringsColorado SpringsUSA

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