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On higher-order differential operators with a regular singularity. (English) Zbl 0837.34027

Summary: A boundary-value problem for the non-self-adjoint differential operators

$\ell y\equiv {y}^{\left(n\right)}+\sum _{j=0}^{n-2}\left(\frac{{\nu }_{j}}{{x}^{n-j}}+{q}_{j}\left(x\right)\right){y}^{\left(j\right)},\phantom{\rule{1.em}{0ex}}0

with a regular singularity at zero is investigated. Theorems are obtained on completeness, on the expansion with respect to the eigen- and associated functions of the boundary-value problem on a finite interval, and on equiconvergence. In addition, the inverse problem is investigated.

##### MSC:
 34B05 Linear boundary value problems for ODE 34A55 Inverse problems of ODE 34B27 Green functions 34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions (ODE)