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AIMS Mathematics

2018, Volume 3, Issue 1: 21-34. doi: 10.3934/Math.2018.1.21
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Research article

Lp-analysis of one-dimensional repulsive Hamiltonian with a class of perturbations

  • 1.
    Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda-shi, Chiba-ken 278-8510, Japan
  • 2.
    Department of Mathematics, Faculty of Science Division I, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, 162-8601, Tokyo, Japan
  • Received: 01 March 2017 Accepted: 22 December 2017 Published: 05 January 2018

  • MSC : 47E05, 47A10

  • The spectrum of one-dimensional repulsive Hamiltonian with a class of perturbations $H_p = -\frac{d^2}{dx^2}-x^2+V(x)$ in $L^p(\mathbb{R})$ ($1 < p < \infty$) is explicitly given. It is also proved that the domain of $H_p$ is embedded into weighted $L^q$-spaces for some $q>p$. Additionally, non-existence of related Schrödinger ($C_0$-)semigroup in $L^p(\mathbb{R})$ is shown when $V(x)\equiv 0$.

    Citation: Motohiro Sobajima, Kentarou Yoshii. Lp-analysis of one-dimensional repulsive Hamiltonian with a class of perturbations[J]. AIMS Mathematics, 2018, 3(1): 21-34. doi: 10.3934/Math.2018.1.21

    Related Papers:

  • The spectrum of one-dimensional repulsive Hamiltonian with a class of perturbations $H_p = -\frac{d^2}{dx^2}-x^2+V(x)$ in $L^p(\mathbb{R})$ ($1 < p < \infty$) is explicitly given. It is also proved that the domain of $H_p$ is embedded into weighted $L^q$-spaces for some $q>p$. Additionally, non-existence of related Schrödinger ($C_0$-)semigroup in $L^p(\mathbb{R})$ is shown when $V(x)\equiv 0$.


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  • © 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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