Analytic Hypoellipticity and the Treves Conjecture
We are concerned with the problem of the analytic hypoellipticity; precisely, we focus on the real analytic regularity of the solutions of sums of squares with real analytic coefficients. Treves conjecture states that an operator of this type is analytic hypoelliptic if and only if all the strata in...
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| Format: | Article |
| Language: | English |
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University of Bologna
2016-12-01
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| Series: | Bruno Pini Mathematical Analysis Seminar |
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| Online Access: | https://mathematicalanalysis.unibo.it/article/view/6690 |
| _version_ | 1818603734526066688 |
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| author | Marco Mughetti |
| author_facet | Marco Mughetti |
| author_sort | Marco Mughetti |
| collection | DOAJ |
| description | We are concerned with the problem of the analytic hypoellipticity; precisely, we focus on the real analytic regularity of the solutions of sums of squares with real analytic coefficients. Treves conjecture states that an operator of this type is analytic hypoelliptic if and only if all the strata in the Poisson-Treves stratification are symplectic. We discuss a model operator, P, (firstly appeared and studied in [3]) having a single symplectic stratum and prove that it is not analytic hypoelliptic. This yields a counterexample to the sufficient part of Treves conjecture; the necessary part is still an open problem. |
| first_indexed | 2024-12-16T13:27:53Z |
| format | Article |
| id | doaj.art-0b386d2de78d4492ab2b28199fdfa7e2 |
| institution | Directory Open Access Journal |
| issn | 2240-2829 |
| language | English |
| last_indexed | 2024-12-16T13:27:53Z |
| publishDate | 2016-12-01 |
| publisher | University of Bologna |
| record_format | Article |
| series | Bruno Pini Mathematical Analysis Seminar |
| spelling | doaj.art-0b386d2de78d4492ab2b28199fdfa7e22022-12-21T22:30:10ZengUniversity of BolognaBruno Pini Mathematical Analysis Seminar2240-28292016-12-0171536810.6092/issn.2240-2829/66906087Analytic Hypoellipticity and the Treves ConjectureMarco Mughetti0University of BolognaWe are concerned with the problem of the analytic hypoellipticity; precisely, we focus on the real analytic regularity of the solutions of sums of squares with real analytic coefficients. Treves conjecture states that an operator of this type is analytic hypoelliptic if and only if all the strata in the Poisson-Treves stratification are symplectic. We discuss a model operator, P, (firstly appeared and studied in [3]) having a single symplectic stratum and prove that it is not analytic hypoelliptic. This yields a counterexample to the sufficient part of Treves conjecture; the necessary part is still an open problem.https://mathematicalanalysis.unibo.it/article/view/6690Sums of squares of vector fieldsAnalytic hypoellipticityTreves conjecture |
| spellingShingle | Marco Mughetti Analytic Hypoellipticity and the Treves Conjecture Bruno Pini Mathematical Analysis Seminar Sums of squares of vector fields Analytic hypoellipticity Treves conjecture |
| title | Analytic Hypoellipticity and the Treves Conjecture |
| title_full | Analytic Hypoellipticity and the Treves Conjecture |
| title_fullStr | Analytic Hypoellipticity and the Treves Conjecture |
| title_full_unstemmed | Analytic Hypoellipticity and the Treves Conjecture |
| title_short | Analytic Hypoellipticity and the Treves Conjecture |
| title_sort | analytic hypoellipticity and the treves conjecture |
| topic | Sums of squares of vector fields Analytic hypoellipticity Treves conjecture |
| url | https://mathematicalanalysis.unibo.it/article/view/6690 |
| work_keys_str_mv | AT marcomughetti analytichypoellipticityandthetrevesconjecture |