Abstract
We define the Hermite-Sobolev spaces naturally associated to the harmonic oscillatorH = −δ+|x|2. Structural properties, relations with the classical Sobolev spaces, boundedness of operators and almost everywhere convergence of solutions of the Schrodinger equation are also considered.
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Bongioanni, B., Torrea, J.L. Sobolev spaces associated to the harmonic oscillator. Proc. Indian Acad. Sci. (Math. Sci.) 116, 337–360 (2006). https://doi.org/10.1007/BF02829750
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DOI: https://doi.org/10.1007/BF02829750