ON THE NUMBER OF LINEARLY INDEPENDENT QUADRATICALLY INTEGRABLE SOLUTIONS OF DIFFERENTIAL EQUATIONS
we consider the equation l[y] - Cλy = 0 in the finite-dimensional Hilbert space, where l is a formal self adjoint expression, Сλ = Cλ(t) is a Nevanlinna operator function of λ for almost fixed t. We prove that the number of linearly independent quadratically integrable with weight (Ιmλ)-1ΙmCλ solutions of this equation does not depend of λ for Ιπmλ >0 and for Ιmλ The proof rests on the constancy (for Ιmλ >0 and for Ιmλ ) of deficiency numbers of the family of minimal linear relations that are associated with this equation.