Recursion relations and the asymptotic behavior of the eigenvalues of the laplacian
Compositio Mathematica, Volume 38 (1979) no. 2, p. 201-240
@article{CM_1979__38_2_201_0,
     author = {Gilkey, Peter B.},
     title = {Recursion relations and the asymptotic behavior of the eigenvalues of the laplacian},
     journal = {Compositio Mathematica},
     publisher = {Sijthoff et Noordhoff International Publishers},
     volume = {38},
     number = {2},
     year = {1979},
     pages = {201-240},
     zbl = {0405.58050},
     mrnumber = {528840},
     language = {en},
     url = {http://www.numdam.org/item/CM_1979__38_2_201_0}
}
Gilkey, Peter B. Recursion relations and the asymptotic behavior of the eigenvalues of the laplacian. Compositio Mathematica, Volume 38 (1979) no. 2, pp. 201-240. http://www.numdam.org/item/CM_1979__38_2_201_0/

[1] M. Atiyah, R. Bott and V.K. Patodi: On the heat equation and the index theorem. Invent. Math. 19 (1973) 279-330. | MR 650828 | Zbl 0257.58008

[2] M. Atiyah, R. Bott and A. Shapiro: Clifford Modules. Topology 3 (1963) 3-38. | MR 167985 | Zbl 0146.19001

[3] M. Atiyah, V.K. Patodi and I.M. Singer: Spectral asymmetry and Riemannian geometry. Bull. Lond. Math. Soc. 5 (1973) 229-234. | MR 331443 | Zbl 0268.58010

[4] M. Berger: Sur le spectre d'une variété Riemannienne. C.R. Acad. Sci. Paris 263 (1963) 13-16. | Zbl 0141.38203

[5] S. Chern: A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds. Ann. Math. 45 (1944) 747-752. | MR 11027 | Zbl 0060.38103

[6] H. Donnely and V.K. Patodi: Spectrum and fixed point set of isometries II. Topology 16 (1977) 1-12. | MR 433513 | Zbl 0341.53023

[7] D. Epstein: Natural Tensors on Riemannian Manifolds. J. Diff. Geo 10 (1973) 631-646. | MR 415531 | Zbl 0321.53039

[8] P. Gilkey: Curvature and the eigenvalues of the Laplacian for elliptic complexes. Advances in Math. 10 (1973) 344-382. | MR 324731 | Zbl 0259.58010

[9] P. Gilkey: Spectral Geometry of a Riemannian Manifold. J. Diff. Geo. 10 (1975) 601-618. | MR 400315 | Zbl 0316.53035

[10] P. Gilkey: Spectral Geometry of real and complex manifolds. Proc. Symp. Pure and App. Math. 27 (1975) 265-280. | MR 388466 | Zbl 0311.53056

[11] P. Gilkey: Spectral Geometry of symmetric spaces. AMS transactions 225 (1977) 341-353. | MR 423258 | Zbl 0342.35047

[12] P. Gilkey: Lefschetz formulas and the heat equation (to appear).

[13] P. Gilkey: Spectral geometry and the Lefschetz formulas for a holomorphic isometry of an almost complex manifold (to appear).

[14] P. Gilkey: The Boundary Integrand in the formula for the Signature and Euler characteristic of a Riemannian manifold with boundary. Advances in Math. 15 (1975) 334-360. | MR 368084 | Zbl 0306.53042

[15] P. Gilkey: Local invariants of a pseudo-Riemannian manifold. Math. Scand. 36 (1975) 109-130. | MR 375340 | Zbl 0299.53040

[15a] P. Gilkey: Curvature and the heat equation for the Delham complex (to appear).

[16] P. Greiner: An asymptotic expansion for the heat equation. Arch. Rat. Mech. Anal. 41 (1971) 163-218. | MR 331441 | Zbl 0238.35038

[17] T. Kawasaki: The Signature Theorem for V-Manifolds (to appear in Topology). | MR 474432 | Zbl 0392.58009

[18] G. Louchard: Mouvement Brownian et Valeurs propres du Laplacian. Ann. Inst. Henri Poincaré, vol. IV (1968) 331-342. | Numdam | MR 261695 | Zbl 0181.20803

[19] H.P. Mckean and V. Vanmoerbeke: The spectrum of Hill's equation. Invent. Math. 30 (1975) 217-274. | MR 397076 | Zbl 0319.34024

[20] H.P. Mckean and I.M. Singer: Curvature and the eigenforms of the Laplacian. J. Diff. Geo. 1 (1967) 43-69. | MR 217739 | Zbl 0198.44301

[21] V.K. Patodi: Curvature and the eigenforms of the Laplace operator. J. Diff. Geo. 5 (1971) 233-249. | MR 292114 | Zbl 0211.53901

[22] V.K. Patodi: Curvature and the fundamental solution of the heat equation. J. Indian Math. Soc. 34 (1970) 269-285. | MR 488181 | Zbl 0237.53039

[23] T. Sakai: On the eigenvalues of the Laplacian and curvature of Riemannian manifold. Tohuku Math. J. 23 (1971) 585-603. | MR 303465 | Zbl 0237.53040

[24] R.T. Seeley: Complex powers of an elliptic operator. Proc. Symp. Pure and App. Math. 10 (1967) 288-307. | MR 237943 | Zbl 0159.15504

[25] R.T. Seeley: Singular integrals and boundary problems. Amer. J. Math. 88 (1966) 781-809. | MR 209915 | Zbl 0178.17601

[26] P. Stredder: Natural differential operators on Riemannian manifolds and representations of the orthogonal and special orthogonal group. J. Diff. Geo. 10 (1975) 647-660. | MR 415692 | Zbl 0318.53046

[27] H. Weyl: The classical groups. Princeton University Press, Princeton N.J. 1946 (USA). | JFM 65.0058.02 | Zbl 1024.20501