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The authors consider the problem of the determination of a unknown source f=f(x,t) in the heat conduction equation from overspecified data. For certain types of functions f they demonstrate the uniqueness of the unknown source and derive a priori estimates of the continuous dependence upon the data. As an example of the results they state one of their theorems. Let chi (a,b)(x) denote the characteristic function of the interval 00, there exists a constant M>0 such that mod f(t) mod

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ABSTRACT. In this paper we calculate the dual of the spaces of distributions L introduced in [I ]. Then we prove that L is the dual of a subspace of C OR).