The form boundedness criterion for the relativistic Schrödinger operator

Vladimir Maz'ya[1]; Igor Verbitsky

  • [1] Linköping University, Department of Mathematics, Linköping 581-83 (Suède), University of Missouri, Department of Mathematics, Columbia, MO 65211 (USA)

Annales de l’institut Fourier (2004)

  • Volume: 54, Issue: 2, page 317-339
  • ISSN: 0373-0956

Abstract

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We establish necessary and sufficient conditions on the real- or complex-valued potential Q defined on n for the relativistic Schrödinger operator - Δ + Q to be bounded as an operator from the Sobolev space W 2 1 / 2 ( n ) to its dual W 2 - 1 / 2 ( n ) .

How to cite

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Maz'ya, Vladimir, and Verbitsky, Igor. "The form boundedness criterion for the relativistic Schrödinger operator." Annales de l’institut Fourier 54.2 (2004): 317-339. <http://eudml.org/doc/116113>.

@article{Mazya2004,
abstract = {We establish necessary and sufficient conditions on the real- or complex-valued potential $Q$ defined on $\{\mathbb \{R\}\}^n$ for the relativistic Schrödinger operator $\sqrt\{-\Delta \} + Q$ to be bounded as an operator from the Sobolev space $W^\{1/2\}_2 (\{\mathbb \{R\}\}^n)$ to its dual $W^\{-1/2\}_2 (\{\mathbb \{R\}\}^n)$.},
affiliation = {Linköping University, Department of Mathematics, Linköping 581-83 (Suède), University of Missouri, Department of Mathematics, Columbia, MO 65211 (USA)},
author = {Maz'ya, Vladimir, Verbitsky, Igor},
journal = {Annales de l’institut Fourier},
keywords = {relativistic Schrödinger operator; complex-valued potentials; Sobolev spaces},
language = {eng},
number = {2},
pages = {317-339},
publisher = {Association des Annales de l'Institut Fourier},
title = {The form boundedness criterion for the relativistic Schrödinger operator},
url = {http://eudml.org/doc/116113},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Maz'ya, Vladimir
AU - Verbitsky, Igor
TI - The form boundedness criterion for the relativistic Schrödinger operator
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 2
SP - 317
EP - 339
AB - We establish necessary and sufficient conditions on the real- or complex-valued potential $Q$ defined on ${\mathbb {R}}^n$ for the relativistic Schrödinger operator $\sqrt{-\Delta } + Q$ to be bounded as an operator from the Sobolev space $W^{1/2}_2 ({\mathbb {R}}^n)$ to its dual $W^{-1/2}_2 ({\mathbb {R}}^n)$.
LA - eng
KW - relativistic Schrödinger operator; complex-valued potentials; Sobolev spaces
UR - http://eudml.org/doc/116113
ER -

References

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