The Functional Equationf(x+y−xy)+f(xy)=f(x)+f(y)

Aequationes mathematicae -     

Local characterization of massless radiation from point sources

We show that the energy-momentum tensor for the massless fields generated by a multipolar source, confined to a world-line, can be split into a radiation and a bound part, both of them having zero divergence off the source world-line. This allows us to compute in a simple way the energy of radiation emitted by the source. Scalar, vector, and tensor fields are studied. An exact expression for the radiated energy of a spinning electron is exhibited. By analizing a system of two electrons we show that radiation from extended sources cannot be described locally in the manner mentioned above.     

Markov subshifts and partial representation of $$\mathbb{F}_{\text n}$$

In this paper we fix a set * of positive elements of the free group (e. g. the set of finite words occurring in a Markov subshift) as well as n partial isometries on a Hilbert space H. Based on these we define a map S : which we prove to be a partial representation of on H under certain conditions studied by Matsumoto.*Supported by Capes.