Kato's Inequality for Magnetic Relativistic Schr\"odinger Operators

Fumio Hiroshima; Takashi Ichinose; József Lőrinczi

Kato's Inequality for Magnetic Relativistic Schr\"odinger Operators

Analysis of PDEs 2017-02-07 v3

Authors: Fumio Hiroshima , Takashi Ichinose , József Lőrinczi

Abstract

Kato's inequality is shown for the magnetic relativistic Schr\"odinger operator $H_{A,m}$ defined as the operator theoretical {\it square root} of the selfadjoint, magnetic nonrelativistic Schr\"odinger operator $(-i\nabla-A(x))^2+m^2$ with an $L^{2}_{\text{\rm loc}}$ vector potential $A(x)$ .

Keywords

Kato's inequality magnetic relativistic Schrödinger operator square root selfadjoint operator vector potential nonrelativistic Schrödinger operator L^2_loc

Cite

@article{arxiv.1604.03933,
  title  = {Kato's Inequality for Magnetic Relativistic Schr\"odinger Operators},
  author = {Fumio Hiroshima and Takashi Ichinose and József Lőrinczi},
  journal= {arXiv preprint arXiv:1604.03933},
  year   = {2017}
}

Comments

33 pages; to be published in Publ. RIMS Kyoto University, {\bf 53} (2017)

Kato's Inequality for Magnetic Relativistic Schr\"odinger Operators

Abstract

Keywords

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