## Band asymptotics in two dimensions.(English)Zbl 0478.58029

### MSC:

 58J50 Spectral problems; spectral geometry; scattering theory on manifolds 58J40 Pseudodifferential and Fourier integral operators on manifolds 53C20 Global Riemannian geometry, including pinching 58C40 Spectral theory; eigenvalue problems on manifolds 35S05 Pseudodifferential operators as generalizations of partial differential operators 35P15 Estimates of eigenvalues in context of PDEs 35P20 Asymptotic distributions of eigenvalues in context of PDEs
Full Text:

### References:

 [1] de Verdière, Y.Colin, Su le spectre des operateurs elliptiques a bicharacteristiques toutes periodiques, Comment. math. helv., 54, 508-522, (1979) · Zbl 0459.58014 [2] Duistermaat, J.J; Guillemin, V, The spectrum of positive elliptic operators and periodic geodesics, Invent. math., 29, 184-269, (1975) · Zbl 0322.35071 [3] Guillemin, V, Some spectral results for the Laplace operator with potential on the n-sphere, Adv. in math., 27, 273-286, (1978) · Zbl 0433.35052 [4] Guillemin, V, The Radon transform on Zoll surfaces, Adv. in math., 22, 85-119, (1976) · Zbl 0353.53027 [5] Guillemin, V; Sternberg, S, On the spectra of commuting pseudodifferential operators: recent work of Kac-spencer, Weinstein and others, (), 149-165 · Zbl 0502.58036 [6] Guillemin, V; Sternberg, S, Geometric asymptotics, () · Zbl 0503.58018 [7] Hirschowitz, A; Piriou, A, Propriétés de transmission pour LES opérateurs intégraux de Fourier, (1978), preprint, Nice · Zbl 0456.58028 [8] Hörmander, L, The spectral function of an elliptic operator, Acta math., 121, 193-218, (1968) · Zbl 0164.13201 [9] Hörmander, L, Fourier integral operators, I, Acta math., 127, 79-183, (1971) · Zbl 0212.46601 [10] Milnor, J, Morse theory, () [11] Milnor, J, Lectures on the h-cobordism theorem, () [12] Moser, J, On the volume element on a manifold, Trans. amer. math. soc., 120, 286-294, (1965) · Zbl 0141.19407 [13] de Rham, G, Variétés différentiables, (1960), Hermann Paris · Zbl 0089.08105 [14] Winstein, A, Asymptotics of eigenvalue clusters for the Laplacian plus a potential, Duke math. J., 44, 883-892, (1977) · Zbl 0385.58013
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.