Two remarks about spectral asymptotics of pseudodifferential operators

• Autorzy: Wojciech Czaja , Ziemowit Rzeszotnik
• Języki publikacji: EN

Abstrakty

EN

In this paper we show an asymptotic formula for the number of eigenvalues of a pseudodifferential operator. As a corollary we obtain a generalization of the result by Shubin and Tulovskiĭ about the Weyl asymptotic formula. We also consider a version of the Weyl formula for the quasi-classical asymptotics.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 80
• Numer: 1
• Strony: 131-145

Daty

wydano

1999

otrzymano

1998-03-02

poprawiono

1998-06-12

poprawiono

1998-11-27

Twórcy

autor

Wojciech Czaja

• Department of Mathematics, Washington University, Campus Box 1146, St. Louis, Missouri 63130, U.S.A.

autor

Ziemowit Rzeszotnik

• Department of Mathematics, Washington University, Campus Box 1146, St. Louis, Missouri 63130, U.S.A.

Bibliografia

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• [4] P. Głowacki, The Weyl asymptotic formula for a class of pseudodifferential operators, ibid. 127 (1998), 169-170.
• [5] L. Hörmander, On the asymptotic distribution of the pseudodifferential operators in $ℝ^n$, Ark. Mat. 17 (1979), 297-313.
• [6] L. Hörmander, The Analysis of Linear Partial Differential Operators, Springer, Berlin, 1983.
• [7] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
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• [11] M. A. Shubin and V. N. Tulovskiĭ, On the asymptotic distribution of the eigenvalues of pseudodifferential operators in $ℝ^n$, Mat. Sb. 92 (134) (1973), 571-588 (in Russian).