Essential self-adjointness of real principal type operators
Nakamura, Shu1; Taira, Kouichi2
1 Department of Mathematics, Faculty of Sciences, Gakushuin University, 1-5-1, Mejiro, Toshima, Tokyo, (Japan) 171-8588
2 Research Organization of Science and Technology, Ritsumeikan university, Kita Ward, Kyoto, (Japan)
Annales Henri Lebesgue, Volume 4 (2021), pp. 1035-1059.

We study the essential self-adjointness for real principal type differential operators. Unlike the elliptic case, we need geometric conditions even for operators on the Euclidean space with asymptotically constant coefficients, and we prove the essential self-adjointness under the null non-trapping condition.

Nous étudions le caractère essentiellement auto-adjoint pour des opérateurs de type principal réel. Contrairement au cas elliptique, nous avons besoin de conditions géométriques même pour des opérateurs sur l’espace euclidien avec coefficients asymptotiquement constants, et nous démontrons le caractère essentiellement auto-adjoint sous la condition de non-capture à énergie zéro.

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Revised:
Accepted:
Published online:
DOI: 10.5802/ahl.96
Classification: 58J50, 35P25, 47B25
Mots-clés : Principal type operators, essential self-adjointness, non-trapping conditions
Nakamura, Shu 1; Taira, Kouichi 2

1 Department of Mathematics, Faculty of Sciences, Gakushuin University, 1-5-1, Mejiro, Toshima, Tokyo, (Japan) 171-8588
2 Research Organization of Science and Technology, Ritsumeikan university, Kita Ward, Kyoto, (Japan) 
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Nakamura, Shu; Taira, Kouichi. Essential self-adjointness of real principal type operators. Annales Henri Lebesgue, Volume 4 (2021), pp. 1035-1059. doi : 10.5802/ahl.96. http://www.numdam.org/articles/10.5802/ahl.96/

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