Convex domains and linear combinations of continuous functions
I. J. Schoenberg · Bulletin of the American Mathematical Society · 1933
Annales de l'École Normale, (3), vol.28, pp.56-57.It can be derived immediately from some fundamental properties of convex domains to be found in Chapter I of C. Carathéodory's article Über den Variabilitatsbereich der Fourierschen Konstanten von positiven harmonischen Funktionen, Rendiconti di Palermo, vol.32 (1911), pp.193-217.The reader is referred to this place for all the information about convex domains which is used in this note.{ Concerning this assumption on p(x) see the concluding remark at the end of this note.