In this paper we characterize compactness of the canonical solution operator to $\Bar{\partial}$ on weigthed $L^{2}$ spaces on $\mathbb{C}$. For this purpose we consider certain Schrödinger operators with magnetic fields and use a condition which is equivalent to the property that these operators have compact resolvents. We also point out what are the obstructions in the case of several complex variables.
Publié le : 2006-05-15
Classification:
32W05,
35N15,
47B38,
47F05
@article{1250281775,
author = {Haslinger, Friedrich},
title = {Magnetic Schr\"odinger operators and the $\overline{\partial}$-equation},
journal = {J. Math. Kyoto Univ.},
volume = {46},
number = {4},
year = {2006},
pages = { 249-257},
language = {en},
url = {http://dml.mathdoc.fr/item/1250281775}
}
Haslinger, Friedrich. Magnetic Schrödinger operators and the $\overline{\partial}$-equation. J. Math. Kyoto Univ., Tome 46 (2006) no. 4, pp. 249-257. http://gdmltest.u-ga.fr/item/1250281775/