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Magnetic Schroedinger operators and the d-bar equation

Friedrich Haslinger
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Abstract

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 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.

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Friedrich Haslinger. 2006-07-03. Magnetic Schroedinger operators and the d-bar equation. https://arxiv.org/abs/math/0607047

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