Displaying similar documents to “The spectral distribution of a globally elliptic operator”

The level crossing problem in semi-classical analysis I. The symmetric case

Yves Colin de Verdière (2003)

Annales de l’institut Fourier

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We describe a microlocal normal form for a symmetric system of pseudo-differential equations whose principal symbol is a real symmetric matrix with a generic crossing of eigenvalues. We use it in order to give a precise description of the microlocal solutions.

Semiclassical spectral estimates for Toeplitz operators

David Borthwick, Thierry Paul, Alejandro Uribe (1998)

Annales de l'institut Fourier

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Let X be a compact Kähler manifold with integral Kähler class and L → X a holomorphic Hermitian line bundle whose curvature is the symplectic form of X . Let H ∈ C ∞ ( X , ℝ ) be a Hamiltonian, and let T k be the Toeplitz operator with multiplier H acting on the space ℋ k = H 0 ( X , L ⊗ k ) . We obtain estimates on the eigenvalues and eigensections of T k as k → ∞ , in terms of the classical Hamilton flow of H . We study in some detail the case when X is an integral coadjoint orbit of a Lie group.

General spectral flow formula for fixed maximal domain

Bernhelm Booss-Bavnbek, Chaofeng Zhu (2005)

Open Mathematics

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We consider a continuous curve of linear elliptic formally self-adjoint differential operators of first order with smooth coefficients over a compact Riemannian manifold with boundary together with a continuous curve of global elliptic boundary value problems. We express the spectral flow of the resulting continuous family of (unbounded) self-adjoint Fredholm operators in terms of the Maslov index of two related curves of Lagrangian spaces. One curve is given by the varying domains,...