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.

For the hypoelliptic differential operators $P={\partial }_{x}^{2}+{\left({x}^{k}{\partial }_{y}-{x}^{l}{\partial }_{t}\right)}^{2}$ 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 $\left(k,l\right)=\left(0,1\right)$), 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},
pages = {21--45},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 2},
number = {1},
year = {2003},
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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