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On higher-order differential operators with a regular singularity. (English. Russian original) Zbl 0837.34027
Summary: A boundary-value problem for the non-self-adjoint differential operators $$\ell y \equiv y^{(n)} + \sum^{n - 2}_{j = 0} \left( {\nu_j \over x^{n - j}} + q_j(x) \right) y^{(j)}, \quad 0 < x < T,$$ 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.

34B05Linear boundary value problems for ODE
34A55Inverse problems of ODE
34B27Green functions
34L10Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions (ODE)
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