Around supersymmetry for semiclassical second order differential operators
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Abstract:
Let $P(h),h\in ]0,1]$ be a semiclassical scalar differential operator of order $2$. The existence of a supersymmetric structure given by a matrix $G(x;h)$ was exhibited by Hérau, Hitrik, and Sjöstrand (2011) under rather general assumptions. In this paper we give a sufficient condition on the coefficients of $P(h)$ so that the matrix $G(x;h)$ enjoys some nice estimates with respect to the semiclassical parameter.References
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Additional Information
- Laurent Michel
- Affiliation: Laboratoire J.-A. Dieudonné, Université de Nice
- MR Author ID: 354828
- Email: lmichel@unice.fr
- Received by editor(s): June 24, 2015
- Received by editor(s) in revised form: November 23, 2015
- Published electronically: March 17, 2016
- Communicated by: Michael Hitrik
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 4487-4500
- MSC (2010): Primary 81Q20, 81Q60; Secondary 47A75, 35P15
- DOI: https://doi.org/10.1090/proc/13053
- MathSciNet review: 3531196