Representations of initial heat distributions by means of their heat distributions as functions of time

In the heat distribution u(t, x), on the whole n-dimensional space R-n, whi ch is given as the solution of the heat equation on R+ x R-n with an initia l heat distribution F is an element of L-2(R-n, dx), it is shown that F is determined and simply represented by the observations u(t, x(1),x') and partial derivative u(t, x(1), x')/partial derivative x(1) for x' - (x(2), ..., x(n)) is an element of Rn-1 and t>0, at any fixed poin t x(1).