The Weyl asymptotic formula by the method of Tulovskiĭ and Shubin

Głowacki, Paweł

Studia Mathematica, Tome 129 (1998), p. 169-190 / Harvested from The Polish Digital Mathematics Library

Résumé

Let A be a pseudodifferential operator on $ℝ^{N}$ whose Weyl symbol a is a strictly positive smooth function on $W = ℝ^{N} \times ℝ^{N}$ such that $| \partial^{α} a | \leq C_{α} a^{1 - ϱ}$ for some ϱ>0 and all |α|>0, $\partial^{α} a$ is bounded for large |α|, and $l i m_{w \to \infty} a (w) = \infty$ . 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.

Publié le : 1998-01-01

Zbl 0905.47040

EUDML-ID : urn:eudml:doc:216465

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     author = {Pawe\l\ G\l owacki},
     title = {The Weyl asymptotic formula by the method of Tulovski\u\i\ and Shubin},
     journal = {Studia Mathematica},
     volume = {129},
     year = {1998},
     pages = {169-190},
     zbl = {0905.47040},
     language = {en},
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Głowacki, Paweł. The Weyl asymptotic formula by the method of Tulovskiĭ and Shubin. Studia Mathematica, Tome 129 (1998) pp. 169-190. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv127i2p169bwm/

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