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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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