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A simple criterion for essential self-adjointness of Weyl pseudodifferential operators

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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OriginalspracheEnglisch
Aufsatznummer38
FachzeitschriftJournal of Pseudo-Differential Operators and Applications
Jahrgang16
Ausgabenummer2
Frühes Online-Datum23 Mai 2025
PublikationsstatusVeröffentlicht - Juni 2025

Abstract

We prove a new criterion for essential self-adjointness of pseudodifferential operators, which does not involve ellipticity-type assumptions. Essential self-adjointness is proved for symbols in C2d+3 with derivatives of order two and higher being uniformly bounded. These results also apply to hermitian operator-valued symbols on infinite-dimensional Hilbert spaces, which are important to applications in physics. Our method relies on a phase space differential calculus for quadratic forms on L2(Rd), Calderón-Vaillancourt type theorems and a recent self-adjointness result for Toeplitz operators.

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A simple criterion for essential self-adjointness of Weyl pseudodifferential operators. / Fulsche, Robert; van Luijk, Lauritz.
in: Journal of Pseudo-Differential Operators and Applications, Jahrgang 16, Nr. 2, 38, 06.2025.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Fulsche R, van Luijk L. A simple criterion for essential self-adjointness of Weyl pseudodifferential operators. Journal of Pseudo-Differential Operators and Applications. 2025 Jun;16(2):38. Epub 2025 Mai 23. doi: 10.1007/s11868-025-00699-2, 10.48550/ARXIV.2304.07153
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