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Continuity properties of integral kernels associated with Schrodinger operators on manifolds

机译:流形上与薛定inger算子相关的积分核的连续性

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摘要

For Schrodinger operators (including those with magnetic fields) with singular scalar potentials on manifolds of bounded geometry, we study continuity properties of some related integral kernels: the heat kernel, the Green function, and also kernels of some other functions of the operator. In particular, we show the joint continuity of the heat kernel and the continuity of the Green function outside the diagonal. The proof makes intensive use of the Lippmann-Schwinger equation.
机译:对于有限几何流形上具有奇异标量势的Schrodinger算子(包括具有磁场的算子),我们研究了一些相关积分核的连续性:热核,格林函数以及该算子的其他一些函数的核。特别是,我们显示了热核的联合连续性和对角线外部的格林函数的连续性。该证明大量使用了Lippmann-Schwinger方程。

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