An explicit kernel K_H built from the Hamiltonian controls the Stieltjes transform of the eigenvalue counting function up to constants, yielding trace-class and sparse-spectrum criteria.
Reiffenstein, A quantitative formula for the imaginary part of a Weyl coefficient, J
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Eigenvalue distribution of canonical systems: trace class and sparse spectrum
An explicit kernel K_H built from the Hamiltonian controls the Stieltjes transform of the eigenvalue counting function up to constants, yielding trace-class and sparse-spectrum criteria.