Analytic smoothing effect for the Schrödinger equation relative to the harmonic oscillator equation

We study the microlocal analytic smoothing effect for the solutions of the Schrödinger equation associated with the harmonic oscillator using the method of Martinez, Nakamura and Sordoni (Comm. Pure Appl. Math. 59 (2006), 1330–1351) of microlocal weights estimates.