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Let {zi}i=1 denote n complex variables. Let z = (z1, . . . , zn), D = (D1, . . . , Dn) with Djφ(z) = ∂φ(z)/∂zj , and let P (D) be a multinomial partial differential operator in the Dj . Using complex translations and quasi inner products, solutions are constructed for initial value generalized heat problems of the form Ht(z, t) = P (D)H(z, t), H(z, 0) = φ(z) in which φ(z) is entire with suitable growth. Growth bounds are obtained for the H(z, t) and these, in turn, are used to construct solutions of higher order and other types of wellposed and ill-posed evolution problems. Applications are given for special equations.

Complex transformations of solutions of generalized initial value heat problems