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Second term of the spectral asymptotic expansion of the Laplace-Beltrami operator on manifolds with boundary. (English) Zbl 0453.35068

MSC:
35P20 Asymptotic distributions of eigenvalues in context of PDEs
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35P99 Spectral theory and eigenvalue problems for partial differential equations
35L05 Wave equation
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[9] L. H?rmander, ”Fourier integral operators,” Acta Math.,127, 79-183 (1971). · Zbl 0212.46601 · doi:10.1007/BF02392052
[10] L. H?rmander, ”The spectral function of an elliptic operator,” Acta Math.,121, No. 1-2, 193-218 (1978). · Zbl 0164.13201 · doi:10.1007/BF02391913
[11] R. B. Melrose and J. Sj?strand, ”Singularities of boundary value problems. I,” Commun. Pure Appl. Math.,31, 593-617 (1978). · Zbl 0378.35014 · doi:10.1002/cpa.3160310504
[12] R. Seely, ”A sharp asymptotic remainder estimate for the eigenvalues of the Laplacian in a domain in R3,” Adv. Math.,29, No. 2, 244-269 (1978). · Zbl 0382.35043 · doi:10.1016/0001-8708(78)90013-0
[13] H. Weyl, ”?ber die asymptotische Verteilung der Eigenwerte,” G?ttinger Nachr., 110-117 (1911).
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