Failure of analytic hypoellipticity in a class of PDOs

2002/12/12 by O Costin, Costin, O, R D Costin +1
Mathematics · #35H10 #35P20 #47F05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:35H10 #msc:35P20 #msc:47F05

paper · pdf · doi:10.48550/arxiv.math/0212167

arxiv created 2002/12/12 · arxiv updated 2009/11/30

Abstract

For the hypoelliptic differential operators P=∂²_ x+(x^k∂_ y -x^l∂_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 \emanalytic 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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