Failure of analytic hypoellipticity in a class of differential operators
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 2 (2003) no. 1, p. 21-45
For the hypoelliptic differential operators P= x 2 +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 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.
Classification:  35B65
@article{ASNSP_2003_5_2_1_21_0,
     author = {Costin, Ovidiu and Costin, Rodica D.},
     title = {Failure of analytic hypoellipticity in a class of differential operators},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 2},
     number = {1},
     year = {2003},
     pages = {21-45},
     zbl = {1150.35018},
     mrnumber = {1990973},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2003_5_2_1_21_0}
}
Costin, Ovidiu; Costin, Rodica D. Failure of analytic hypoellipticity in a class of differential operators. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 2 (2003) no. 1, pp. 21-45. http://www.numdam.org/item/ASNSP_2003_5_2_1_21_0/

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