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Sobolev spaces associated to the harmonic oscillator

B Bongioanni·J L Torrea
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Abstract

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

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B Bongioanni, J L Torrea. 2006-08-28. Sobolev spaces associated to the harmonic oscillator. https://arxiv.org/abs/math/0608684

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