In this paper we characterize those functions f of the real line to itself such that the nonlinear superposition operator Tf defined by Tf [g] := f◦g maps the Hölder-Zygmund space Cs(Rn) to itself, is continuous, and is r times continuously differentiable. Our characterizations cover all cases in which s is real and s > 0, and seem to be novel when s > 0 is an integer.

The Shell model Monte Carlo (SMMC) method [1] was developed as an alternative to direct diagonalization in order to study low-energy nuclear properties. It was successfully applied to nuclear problems where large model spaces made diagonalization impractical. One calculates the thermal canonical expectation values of observables of few-body operators by representing the imaginary-time many-body...

We deal with C(n)-almost periodic functions taking values in a Banach space. We give several properties of such functions, in particular, we investigate their behavior in view of differentiation as well as integration. The superposition operator acting in the space of such functions is also under consideration. Some applications to ordinary as well as partial differential equations are presente...

Fundamental problems of quantum field theory related to the representation problem of canonical commutation relations are discussed within a gauge field version of a van Hove-type model. The Coulomb field generated by a static charge distribution is described as a formal superposition of time-like pseudo-photons in Fock space with a Krein structure. In this context, a generalization of operator...

Here is presented a complete work on the (1+1) dimensional SU(N) YangMills theory with static sources. By studying the structure of the SU(N) group and of the Gauss’ law we construct in the electric representation the appropriate wave functionals, which are simultaneously eigenstates of the Gauss’ operator and of the Hamiltonian. Special consideration has been given on the Fourier transformatio...

The basic concepts of classical mechanics are given in the operator form. The dynamical equation for a hybrid system, consisting of quantum and classical subsystems, is introduced and analyzed in the case of an ideal nonselective measurement. The nondeterministic evolution is found to be the consequence of the superposition of two different deterministic evolutions. Pacs numbers: 03.65.Bz Types...

This paper deals with the probabilistic modeling of an environment that a robot has to navigate in. We use a method for the probabilistic modeling of space called the Bayesian Map formalism. This formalism allows incremental building of models: we define the Superposition operator, which is a formally well-defined operator. We present first a syntactic version of this operator, and second, a ve...

The antilinear operator representation of bipartite pure states of the relative state formulation of quantum mechanics is applied to describe quantum teleportation schemes utilizing an arbitrary pure state as the entangled resource. Bennett type teleportation schemes with nonmaximally entangled pure states are characterized and the notion of ‘entanglement matching’ is introduced in general. Exa...

The basic concepts of classical mechanics are given in the operator form. The dynamical equation for a hybrid system, consisting of quantum and classical subsystems, is introduced and analyzed in the case of an ideal nonselective measurement. The nondeterministic evolution is found to be the consequence of the superposition of two different deterministic evolutions. Pacs numbers: 03.65.Bz Types...

We derive a class of localized solutions of a 2+1 nonlinear Schrödinger (NLS) equation and study their dynamical properties. The ensuing dynamics of these configurations is a superposition of a uniform, “center of mass” motion and a slower, individual motion; as a result, nontrivial scattering between humps may occur. Spectrally, these solutions correspond to the discrete spectrum of a certain ...