ON SQUARE ROOT OF STURM-LIUVILLE OPERATOR
Ключевые слова:Sturm-Liouville operator, square root of operator, functional differential operator, equations with deviating argument, Kato hypothesis, Macintosh example, Gours operator, inverse problem, spectrum, eigenvalues, eigenfunctions, unitary operator, similarity operator.
In this paper, we find square root of the Sturm – Liouville operator and show that this root is a
functional-differential operator of first-order. Form of the corresponding boundary problem of this functional -
differential equation is found. As a suggestive idea, we use one Putnam theorem. Boundary value conditions of the
Sturm-Liouville operator have a very special form, and they are dictated by the method of investigation. The found
unitary operator generalizes the known momentum operator.