Algebras with general commutation relations and their applications. II. Unitary-nonlinear operator equations

Various aspects of the calculus of functions of ordered self-adjoint operators are considered. Passage to the commutative limit in the case of general nonlinear commutation relations is studied. An asymptotic solution of the Cauchy problem and asymptotically self-similar solutions are constructed for unitary-nonlinear operator equations. Asymptotic solutions are found for the Hartree equation with Coulomb interaction.Translated from Itogi Nauki i Tekhniki, Sovremennye Problemy Matematiki, Vol. 13, pp. 145–267, 1979.