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On unconditional basisness of the system of eigen and adjoint functions of a differential operator of first order in spaces of vector functions. (Russian. English summary) Zbl 0763.47017
Summary: By using the explicit form of boundary conditions the question of the absolute basisness of the system of eigenfunctions and adjoint functions of the first order differential operator \(Lu=u'+q(x)u\) is studied. The operator \(L\) with the matrix complex-valued potential is considered on the space \(L_ 2(G)\) of vector functions on a finite interval \((-R,R)\).

MSC:
47E05 General theory of ordinary differential operators
34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
46E40 Spaces of vector- and operator-valued functions
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