Schrödinger equation and the oscillatory semigroup for the Hermite operator

We discuss the regularity of the oscillatory semigroup eitH, where H = − + |x|2 is the n-dimensional Hermite operator. The main result is a Strichartz-type estimate for the oscillatory semigroup eitH in terms of the mixed Lp spaces. The result can be interpreted as the regularity of solution to the Schrödinger equation with potential V (x) = |x|2. © 2005 Elsevier Inc. All rights reserved