ABSTRACT

In Theorem 3.15, we gave several necessary and sufficient conditions for a temperature u on R̲n × ]0, a[ to have the Gauss-Weierstrass representation. It is therefore possible to know that a particular temperature is the Gauss-Weierstrass integral of some signed measure, without knowing what the measure is. In this chapter, we show how the measure is determined by the temperature. Of course, in Chapters V and VI we did this in various ways, but only in special cases where the temperature satisfied certain additional conditions. We now treat the general case, where the temperature is assumed only to belong to the class Ra of Chapter III.