Sobolev spaces associated to the harmonic oscillator.

Abstract

We define the Hermite Sobolev spaces naturally associated to the harmonic oscillator $H= -\Delta +|x|^2.$ Structural properties, relations with the classical Sobolev spaces, boundedness of operators and almost everywhere convergence of solutions of the Schrödinger equation are also considered.


Published: Proc. Indian Acad. Sci. Math. Sci. 116 (2006), no. 3, 337--360.