The observations of the companion paper are extended to the case of an infinite number of degrees of freedom. It is shown that classical dynamical systems with square integrable solutions can be described by an abstract, Schrödinger-like equation in a Hilbert space.

It is shown that classical birth and death processes can be described by a Hilbert space, Schrödinger-like equation with the Hamiltonian (a non-Hermitian one) expressed in terms of Bose creation and annihilation operators. A new algebraic method of solving the master equations of birth and...

It is shown that the linear recurrences of the form xn + 1 = ƒ(xn), where ƒ is analytic in xn, can be brought down to a linear recurrence in Hilbert space with the boson displacement operator.

A new method of determining Bäcklund transformations for nonlinear partial differential equations of the evolution type is introduced. Using the Hilbert space approach the problem of finding Bäcklund transformations is brought down to the solution of an abstract equation in Hilbert space.

It is shown that classical dynamical systems can be described by a Hilbert space, Schrödinger-like equation with the Hamiltonian (a non-Hermitian one) expressed in terms of Bose creation and annihilation operators. The presented formalism includes the Carleman embedding as the special case.

A new method for the linearization of non-linear dynamical systems with both a finite and an infinite number of degrees of freedom is introduced. Using the Hilbert space approach the problem of finding the linearization transformations is reduced to the solution of abstract linear equations in...