Uniqueness in Cauchy Problems for Hyperbolic Differential Operators

In this paper we prove a unique continuation theorem for second order strictly hyperbolic differential operators. Results also hold for higher order operators if the hyperbolic cones are strictly convex. These results are proved via certain Carleman inequalities. Unlike [6], the parametrices involved only have real phase functions, but they also have Gaussian factors. We estimate the parametrices and associated remainders using sharp ${L^p}$ estimates for Fourier integral operators which are due to Brenner [1] and Seeger, Stein, and the author [5].