Magnetic Schroedinger operators and the d-bar equation

Details Magnetic Schroedinger operators and the d-bar equation Magnetic Schroedinger operators and the d-bar equation

2006-07-03

arxiv.org/abs/math/0607047v1

Mathematics

Complex Variables

9 pages

Scientific paper

In this paper we characterize compactness of the canonical solution operator to d-bar on weigthed $L^2$ spaces on $\mathbb C.$ For this purpose we consider certain Schr\"odinger 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.

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