Schrodinger equation and the oscillatory semigroup for the Hermite operator

摘要

We discuss the regularity of the oscillatory semigroup e(itH), where H = -Delta + vertical bar x vertical bar(2) is the n-dimensional Hermite operator. The main result is a Strichartz-type estimate for the oscillatory semigroup e(itH) in terms of the mixed LP spaces. The result can be interpreted as the regularity of solution to the Schrodinger equation with potential V(X) = vertical bar x vertical bar(2). (c) 2005 Elsevier Inc. All rights reserved.