Sobolev spaces associated to the harmonic oscillator

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 Schr\"odinger equation are also conside...

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Bibliographic Details
Published in:arXiv.org 2006-08
Main Authors: Bongioanni, B, Torrea, J L
Format: Article
Language:English
Subjects:
Eulers equations
Oscillators
Online Access:Get full text
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Summary: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 Schr\"odinger equation are also considered.
ISSN:2331-8422