Abstract
We consider the effect of a magnetic field for the asymptotic behavior of the trace of the heat kernel for the Schrödinger operator. We discuss the case where the operator has compact resolvents in spite of the fact that the electric potential is degenerate on some submanifold. According to the degree of the degeneracy, we obtain non-classical asymptotics.
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Aramaki, J., Nurmuhammad, A. NON-CLASSICAL ASYMPTOTICS OF THE TRACE OF THE HEAT KERNEL FOR THE MAGNETIC SCHRÖDINGER OPERATOR. Acta Mathematica Hungarica 94, 155–172 (2002). https://doi.org/10.1023/A:1015666823207
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DOI: https://doi.org/10.1023/A:1015666823207