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

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-127-2-169-190

Paweł Głowacki 1

1 
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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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