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Precise eigenvalue asymptotics for transversally elliptic operators. (English) Zbl 0643.35075
Current topics in partial differential equations, Pap. dedic. S. Mizohata Occas. 60th Birthday, 55-62 (1986).
[For the entire collection see Zbl 0604.00006.]
Precise eigenvalue asymptotics for a self-adjoint maximally hypoelliptic (with the loss of m/2 derivatives) operator $$A\in L^{M,m}(X,\Sigma,E)$$ is presented where X is a compact closed manifold with a density, E is a fibering over X, $$\Sigma$$ is a conic symplectic submanifold of $$T^*X$$, m is an order of zero at $$\Sigma$$ of the principal symbol a of A, a is of Mth order positively homogeneous symbol and lower order terms of A satisfy natural vanishing conditions at $$\Sigma$$, $$M>m/2$$.
Reviewer: V.Ivrij
##### MSC:
 35P20 Asymptotic distributions of eigenvalues in context of PDEs 65H10 Numerical computation of solutions to systems of equations 58J50 Spectral problems; spectral geometry; scattering theory on manifolds
Zbl 0604.00006