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AbstractIn this article, we consider the Schrödinger semigroup for the Laplacian Δ on ℝn{\mathbb{R}^{n}}, and characterizethe image of a Sobolev space in L2(ℝn,eu2du){L^{2}(\mathbb{R}^{n},e^{u^{2}}du)}under this semigroup as weighted Bergman space (up to equivalence of norms). Also we have a similar characterization for Hermite Sobolev spaces under the Schrödinger semigroup associated to the Hermite operator H on ℝn{\mathbb{R}^{n}}.
Advances in Pure and Applied Mathematics – de Gruyter
Published: Jan 1, 2019
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