The return map for a planar vector field with nilpotent linear part: a direct and explicit derivation.
Power and exponential-power series solutions of evolution equations
Failure of analytic hypoellipticity in a class of differential operators
For the hypoelliptic differential operators introduced by T. Hoshiro, generalizing a class of M. Christ, in the cases of and left open in the analysis, the operators also fail to be analytic hypoelliptic (except for ), 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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