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.
@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}, mrnumber = {1990973}, zbl = {1150.35018}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2003_5_2_1_21_0/} }
TY - JOUR AU - Costin, Ovidiu AU - Costin, Rodica D. TI - Failure of analytic hypoellipticity in a class of differential operators JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2003 SP - 21 EP - 45 VL - 2 IS - 1 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_2003_5_2_1_21_0/ LA - en ID - ASNSP_2003_5_2_1_21_0 ER -
%0 Journal Article %A Costin, Ovidiu %A Costin, Rodica D. %T Failure of analytic hypoellipticity in a class of differential operators %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2003 %P 21-45 %V 2 %N 1 %I Scuola normale superiore %U http://www.numdam.org/item/ASNSP_2003_5_2_1_21_0/ %G en %F 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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