The inverse Laplacian on the torus has traces given by zeta and lattice sums, and a d-star coupled version is trace class only for powers above the quadratic case.
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The Inverse Laplacian: Traces in Infinite Dimensions
The inverse Laplacian on the torus has traces given by zeta and lattice sums, and a d-star coupled version is trace class only for powers above the quadratic case.