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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
Citations:
Zbl 0604.00006