Sobolev spaces associated to the harmonic oscillator

Details Sobolev spaces associated to the harmonic oscillator Sobolev spaces associated to the harmonic oscillator

2006-08-28

arxiv.org/abs/math/0608684v1

Mathematics

Combinatorics

24 pages

Scientific paper

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.

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