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On the images of Sobolev spaces under the Schrödinger semigroup

Authors
  • C, Sivaramakrishnan
  • D, Sukumar
  • Dogga, Venku Naidu
Type
Published Article
Journal
Advances in Pure and Applied Mathematics
Publisher
De Gruyter
Publication Date
Jan 20, 2018
Volume
10
Issue
1
Pages
65–79
Identifiers
DOI: 10.1515/apam-2016-0116
Source
De Gruyter
Keywords
License
Yellow

Abstract

In this article, we consider the Schrödinger semigroup for the Laplacian Δ on ℝ n {\mathbb{R}^{n}} , and characterize the image of a Sobolev space in L 2 ⁢ ( ℝ n , e u 2 ⁢ d ⁢ u ) {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 ℝ n {\mathbb{R}^{n}} .

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