Essential self-adjointness for magnetic Schrödinger operators on non-compact manifolds

Mikhail Shubin[1]

  • [1] Department of Mathematics, Northeastern University, Boston, MA 02115, USA

Séminaire Équations aux dérivées partielles (1998-1999)

  • Volume: 1998-1999, page 1-22

Abstract

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We give a condition of essential self-adjointness for magnetic Schrödinger operators on non-compact Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. This condition is related to the classical completeness of a related classical hamiltonian without magnetic field. The main result generalizes the result by I. Oleinik [29,30,31], a shorter and more transparent proof of which was provided by the author in [41]. The main idea, as in [41], consists in an explicit use of the Lipschitz analysis on the Riemannian manifold and also by additional geometrization arguments which include a use of a metric which is conformal to the original one with a factor depending on the minorant of the electric potential.

How to cite

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Shubin, Mikhail. "Essential self-adjointness for magnetic Schrödinger operators on non-compact manifolds." Séminaire Équations aux dérivées partielles 1998-1999 (1998-1999): 1-22. <http://eudml.org/doc/10965>.

@article{Shubin1998-1999,
abstract = {We give a condition of essential self-adjointness for magnetic Schrödinger operators on non-compact Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. This condition is related to the classical completeness of a related classical hamiltonian without magnetic field. The main result generalizes the result by I. Oleinik [29,30,31], a shorter and more transparent proof of which was provided by the author in [41]. The main idea, as in [41], consists in an explicit use of the Lipschitz analysis on the Riemannian manifold and also by additional geometrization arguments which include a use of a metric which is conformal to the original one with a factor depending on the minorant of the electric potential.},
affiliation = {Department of Mathematics, Northeastern University, Boston, MA 02115, USA},
author = {Shubin, Mikhail},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
pages = {1-22},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Essential self-adjointness for magnetic Schrödinger operators on non-compact manifolds},
url = {http://eudml.org/doc/10965},
volume = {1998-1999},
year = {1998-1999},
}

TY - JOUR
AU - Shubin, Mikhail
TI - Essential self-adjointness for magnetic Schrödinger operators on non-compact manifolds
JO - Séminaire Équations aux dérivées partielles
PY - 1998-1999
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 1998-1999
SP - 1
EP - 22
AB - We give a condition of essential self-adjointness for magnetic Schrödinger operators on non-compact Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. This condition is related to the classical completeness of a related classical hamiltonian without magnetic field. The main result generalizes the result by I. Oleinik [29,30,31], a shorter and more transparent proof of which was provided by the author in [41]. The main idea, as in [41], consists in an explicit use of the Lipschitz analysis on the Riemannian manifold and also by additional geometrization arguments which include a use of a metric which is conformal to the original one with a factor depending on the minorant of the electric potential.
LA - eng
UR - http://eudml.org/doc/10965
ER -

References

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