The Solutions of Important Special Cases of the Equation of Measurement

Abstract

The preceding contribution by Aczél [Acz2] (see also [ARR]) treats the equation

$$u\left( {Ax + p} \right) = R\left( {A,p} \right)u\left( x \right) + P\left( {A,p} \right)$$

((1))

where AɛS≤T_n (IR) (S a certain subring of T_n (IR), the full matrix ring over the real numbers IR), and x, pɛIRn, or xɛIR+, (Ax+p) ɛIR+. In our pre-ceding contribution we called (a slightly more general form of) this functional equation the equation of measurement. To represent the re-sults in a more detailed manner we introduce the following functions.