00-384 [A.A. Balinsky, W.D. Evans and Roger T. Lewis

Sobolev, Hardy and CLR inequalities associated with Pauli operators in $\mathbb{R}^3$ (138K, "Postscript") Oct 2, 00

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Abstract. In a previous article, the first two authors have proved that the existence of zero modes of Pauli operators is a rare phenomenon; inter alia, it is proved that for $|\vec{B}| \in L^{3/2}(\mathbb{R}^3)$, the set of magnetic fields $\vec{B}$ which do not yield zero modes contains an open dense subset of $[L^{3/2}(\mathbb{R}^3)]^3$. Here the analysis is taken further, and it is shown that Sobolev, Hardy and Cwikel-Lieb-Rosenbljum (CLR) inequalities hold for Pauli operators for all magnetic fields in the aforementioned open dense set.

Files: 00-384.src( 00-384.keywords , Sob_Har_CLR.ps )