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