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Remarks on a paper of S. Zelditch: ”Szegoe limit theorems in quantum mechanics”. (English) Zbl 0524.35082


MSC:

35P20 Asymptotic distributions of eigenvalues in context of PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application

Citations:

Zbl 0392.35056
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References:

[1] Beals, R, A general calculus of pseudodifferential operators, Duke math. J., 42, 1-42, (1975) · Zbl 0343.35078
[2] Berezin, F.A, Wick and anti-Wick operators symbols, Math. USSR-sb., 15, 577-606, (1971) · Zbl 0247.47018
[3] Davies, E.B, Classical approximations to Gibbs states, (), 521-527 · Zbl 0456.46056
[4] Helffer, B; Robert, D, Comportement semi-classique du spectre des hamiltoniens quantiques elliptiques, Ann. inst. Fourier (Grenoble), 31, 3, 169-223, (1981) · Zbl 0451.35022
[5] Hormander, L, The Weyl calculus of pseudodifferential operators, Comm. pure appl. math., 32, 359-443, (1979) · Zbl 0388.47032
[6] Hormander, L, On the asymptotic distribution of the eigenvalues of pseudodifferential operators in \(R\)^{n}, Ark. mat., 17, 2, 297-313, (1979) · Zbl 0436.35064
[7] Guillemin, V, Some classical theorems in spectral theory revisited, () · Zbl 0452.35093
[8] Keldys, M.V, On a Tauberian theorem, (), 77-86, [Russian]
[9] Mackey, G.W, Mathematical foundations of quantum mechanics, (1963), Benjamin New York · Zbl 0114.44002
[10] Robert, D, Propriétés spectrales d’opérateurs pseudodifférentiels, Comm. partial differential equations, 3, 9, 755-826, (1978) · Zbl 0392.35056
[11] Robert, D, Comportement asymptotique des valeurs propers d’opérateurs du type Schrödinger à potentiel “dégénéré,”, J. math. pures appl., 61, 275-300, (1982) · Zbl 0511.35069
[12] Tulovskii, V.N; Subin, M.A, On asymptotic distribution of eigenvalues of pseudodifferential operators in \(R\)^{n}, Math. USSR-sb., 21, 4, 565-583, (1973) · Zbl 0295.35068
[13] Widom, H, Eigenvalue distribution theorems for certain homogeneous space, J. funct. anal., 32, 139-147, (1979) · Zbl 0414.43010
[14] Zelditch, S, Szegö limit theorems in quantum mechanics, J. funct. anal., 50, 67-80, (1983) · Zbl 0552.35019
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