Local and global analysis of eigenfunctions

zbMath1176.58017arXiv0903.3420MaRDI QIDQ3536063

Steven Zelditch

Publication date: 17 November 2008

Full work available at URL: https://arxiv.org/abs/0903.3420

zbMATH Keywords

wave equationgeodesic floweigenvalues and eigenfunctionsergodicLaplaciansnodal setRiemannian random waveAnosovfrequency functiondoubling estimatequasimodequantum limit\(L ^p\) normquantum complete integrable

Mathematics Subject Classification ID

Random fields (60G60) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Wave equation (35L05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Pseudodifferential and Fourier integral operators on manifolds (58J40) Ergodic theorems, spectral theory, Markov operators (37A30) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Research exposition (monographs, survey articles) pertaining to global analysis (58-02) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

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