An Analog of Orlov's Theorem on the Deficiency Index of Second-Order Differential Operators

摘要

In [1], Orlov found a class of linear differential operators with real analytic coefficients whose deficiency numbers coincide with the number of roots in the left half-plane of a certain explicitly written polynomial; in [2], it was shown that Orlov's result remains valid for certain operators with nonanalytic coefficients. Later, in [3], among other things, these classes of operators for which Orlov's theorem is true were substantially extended. The aim of this paper is to prove an analog of Orlov's theorem for operators generated by matrix linear second-order quasi-differential expressions.