Problems relating to the asymptotic behaviour in the neighbourhood of the point +infinity and in the neighbourhood of the origin of a solution of an equation l(n)y = lambda y of arbitrary (even or odd) order with complex-valued coefficients are studied. It is assumed here that the coefficients of the quasi-differential expression 1 have the following property: if one reduces the equation l(n)y = lambda y to a system of first-order differential equations, then one can transform that system to a system of differential equations with regular singular point at x = infinity or x = 0. The results obtained allow one to determine the deficiency indices of the corresponding minimal symmetric differential operators and the structure of the spectrum of self-adjoint extensions of these operators.
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