Failure of Analytic Hypoellipticity in a Class of Differential Operators
نویسندگان
چکیده
For the hypoelliptic differential operators P = ∂ x + ( x∂y − x∂t 2 introduced by T. Hoshiro, generalizing a class of M. Christ, in the cases of k and l left open in the analysis, the operators P also fail to be analytic hypoelliptic (except for (k, l) = (0, 1)), in accordance with Treves’ conjecture. The proof is constructive, suitable for generalization, and relies on evaluating a family of eigenvalues of a non-self-adjoint operator.
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