Huygens property of parabolic functions and a uniqueness theorem

It is well known that the zero function is the only non-negative parabolic function (i.e., solution of the heat equation) on R n ×(0,T) which vanishes continuously on R n ×{0} (cf. [2, Part 1, Chap. XVI], [6, Chap. VIII]). In this paper, considering the Huygens property of minimal parabolic functions (see Proposition 2), we shall show the following generalization of the above result