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Around supersymmetry for semiclassical second order differential operators


Author: Laurent Michel
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
Published electronically: March 17, 2016
MathSciNet review: 3531196
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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.


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Additional Information

Laurent Michel
Affiliation: Laboratoire J.-A. Dieudonné, Université de Nice
Email: lmichel@unice.fr

DOI: https://doi.org/10.1090/proc/13053
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
Article copyright: © Copyright 2016 American Mathematical Society

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