Around supersymmetry for semiclassical second order differential operators

Michel, Laurent

doi:10.1090/proc/13053

Around supersymmetry for semiclassical second order differential operators
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Proc. Amer. Math. Soc. 144 (2016), 4487-4500 Request permission

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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