Sobolev spaces associated to the harmonic oscillator
B Bongioanni, J L Torrea
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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