Sobolev spaces associated to the harmonic oscillator |
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| Authors: | B Bongioanni J L Torrea |
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| Institution: | (1) Departamento de Matemática, Facultad de Ingeniería Qímica, Universidad Nacional del Litoral, and Instituto de Matemática Aplicada del Litoral, 3000 Santa Fe, Argentina;(2) Departamento de Matemática, Facultad de Ciencias, Universidad Autónoma de Madrid, Spain |
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| 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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| Keywords: | Hermite operator potential spaces Riesz transforms |
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