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We prove a theorem on uniqueness of determination of a form of first order inside some domain D by its integrals along geodesies of a fixed Riemannian metric connecting an arbitrary pair of points on the boundary of this domain. As an application, this result is used to study the problem of determining the coefficients at lower derivatives in a second order hyperbolic equation.

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Link to this article: http://journals.cambridge.org/abstract_S0956792504005649 How to cite this article: YU. E. ANIKONOV, J. CHENG and M. YAMAMOTO (2004). A uniqueness result in an inverse hyperbolic problem with analyticity.We prove the uniqueness for the inverse problem of determining a coefficient q(x ∈ R n and t > 0, from observations of u| Γ ×(0,T ) and the normal derivative ∂u ∂ν | Γ ×(0,T ) where Γ is an arbitrary C ∞ -hypersurface. Our main result asserts the uniqueness of q over R n provided that T > 0 is sufficiently large and q is analytic near Γ and outside a ball. The proof depends on Fritz John's global Holmgren theorem and the uniqueness by a Carleman estimate.