Analytic hypoellipticity of Keldysh operators

For operators modeled by $ P = x_1 D_{x_1}^2+ D_{x_2}^2+a D_{x_1} $ we show that if $ u $ is smooth and $ Pu$ is analytic then $ u$ is analytic. This is motivated by the question of analyticity of quasinormal modes of black holes across event horizons and is a consequence of a general microlocal result. Joint work with J Galkowski.

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