Geodesic
The Weyl asymptotic formula by the method of Tulovskiĭ and Shubin
Studia Mathematica, Tome 127 (1998) no. 2, pp. 169-190

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Let A be a pseudodifferential operator on $ℝ^N$ whose Weyl symbol a is a strictly positive smooth function on $W = ℝ^N × ℝ^N$ such that $|∂^{α}a| ≤ C_αa^{1-ϱ}$ for some ϱ>0 and all |α|>0, $∂^{α}a$ is bounded for large |α|, and $lim_{w→∞}a(w) = ∞$. Such an operator A is essentially selfadjoint, bounded from below, and its spectrum is discrete. The remainder term in the Weyl asymptotic formula for the distribution of the eigenvalues of A is estimated. This is done by applying the method of approximate spectral projectors of Tulovskiĭ and Shubin. 
Paweł Głowacki. The Weyl asymptotic formula by the method of Tulovskiĭ and Shubin. Studia Mathematica, Tome 127 (1998) no. 2, pp. 169-190. doi: 10.4064/sm-127-2-169-190
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