Research article

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

  • 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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