On the images of Sobolev spaces under the Schrödinger semigroup
2019 ◽
Vol 10
(1)
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pp. 65-79
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Abstract In this article, we consider the Schrödinger semigroup for the Laplacian Δ on {\mathbb{R}^{n}} , and characterize the image of a Sobolev space in {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 {\mathbb{R}^{n}} .
Keyword(s):
Reproducing kernels of Sobolev spaces on ℝd and applications to embedding constants and tractability
2018 ◽
Vol 16
(05)
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pp. 693-715
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2012 ◽
Vol 55
(1)
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pp. 146-152
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2013 ◽
Vol 62
(1)
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pp. 201-233
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2012 ◽
Vol 2012
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pp. 1-15
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2020 ◽
Vol 44
(5)
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pp. 1477-1482