We show that resonant states in scattering on asymptotically hyperbolic manifolds that are analytic near conformal infinity have analytic radiation patterns at infinity. On even asymptotically hyperbolic manifolds, we also show that smooth solutions of Vasy operators with analytic coefficients are also analytic. That answers a question of Zworski ([14] Conjecture 2). The proof is based on previous results of Baouendi–Goulaouic and Bolley–Camus–Hanouzet, and for convenience of the reader, we present an outline of the proof of the latter.

Real Analyticity of Radiation Patterns on Asymptotically Hyperbolic Manifolds

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