ON THE SQUARE ROOT OF THE OPERATOR OF STURM-LIOUVILLE FOURTH-ORDER
Ключевые слова:Kato conjecture, dissipative operator, square root of operator, Putnam theorem, deviating argument, fractional powers of an operator, inverse problem, spectrum, unitary operator, self-adjoint operator, positive operator, functional differential operator, spectral theory.
In the present work found the root of the positive operator of the Sturm - Liouville problem of the
fourth order, which is invertible composition operator of the Sturm - Liouville problem and its adjoint. The found
root does not possess the property of positivity, but is a self-adjoint operator in the essential. One theorem of Putnam
of algebraic character is used as a leading idea. It is hoped that the results will find applications in spectral operator
theory and theoretical physics.