The spectrum of positive elliptic operators and periodic bicharacteristics

Let X be a compact boundaryless C ∞ manifold and let P be a positive elliptic self-adjoint pseudodifferential operator of order m>0 on X. For technical reasons we will assume that P operates on half-densities rather than functions.

[1]  H. Komatsu Theory of microfunctions , 1973 .

[2]  L. Nirenberg,et al.  Lectures on linear partial differential equations , 1973 .

[3]  V. I. Arnol'd,et al.  Characteristic class entering in quantization conditions , 1967 .

[4]  J. Chazarain Formule de Poisson pour les variétés riemanniennes , 1974 .

[5]  L. Hörmander Fourier integral operators. I , 1995 .

[6]  V. K. Patodi,et al.  On the heat equation and the index theorem , 1973 .

[7]  L. Hörmander,et al.  The spectral function of an elliptic operator , 1968 .

[8]  K. G. Andersson Analytic wave front sets for solutions of linear differential equations of principal type , 1973 .

[9]  E. Wright,et al.  An Introduction to the Theory of Numbers , 1939 .

[10]  J. Duistermaat On the Morse index in variational calculus , 1976 .

[11]  S. Minakshisundaram,et al.  Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds , 1949, Canadian Journal of Mathematics.

[12]  M. Atiyah,et al.  A Lefschetz Fixed Point Formula for Elliptic Complexes: I , 1967 .

[13]  Jean-Pierre Serre A Course in Arithmetic , 1973 .

[14]  L. Hörmander Linear Partial Differential Operators , 1963 .

[15]  F. Takens,et al.  Generic properties of geodesic flows , 1972 .

[16]  Robert T. Seeley,et al.  THE RESOLVENT OF AN ELLIPTIC BOUNDARY PROBLEM. , 1969 .

[17]  Raoul Bott,et al.  On the iteration of closed geodesics and the sturm intersection theory , 1956 .

[18]  P. Goldbart,et al.  Linear differential operators , 1967 .

[19]  Y. C. Verdière,et al.  Spectre du laplacien et longueurs des géodésiques périodiques. II , 1973 .

[20]  Robert T. Seeley,et al.  Complex powers of an elliptic operator , 1967 .