Spectral theory of pseudodifferential operators of degree 0 and an application to forced linear waves

DOI10.2140/apde.2020.13.1521zbMath1452.35026arXiv1804.03367OpenAlexW4324262296MaRDI QIDQ2210880

Yves Colin de Verdière

Publication date: 9 November 2020

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.03367

zbMATH Keywords

attractorsspectral theorylimiting absorption principleMorse-Smale propertyinternal wavesinertial wavesescape functionsMourre theoryforced waves

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations (35Q30) Internal waves for incompressible inviscid fluids (76B55) Pseudodifferential and Fourier integral operators on manifolds (58J40) Resonance in context of PDEs (35B34) Stratification effects in inviscid fluids (76B70)

Related Items

Eigenvalue asymptotics for polynomially compact pseudodifferential operators ⋮ Discrete spectrum of zero order pseudodifferential operators ⋮ Radial source estimates in Hölder-Zygmund spaces for hyperbolic dynamics ⋮ Characterization of singular flows of zeroth-order pseudo-differential operators via elliptic eigenfunctions: a numerical study ⋮ The scattering matrix for 0th order pseudodifferential operators ⋮ Curvature contribution to the essential spectrum of Dirac operators with critical shell interactions ⋮ Space-time statistics of a linear dynamical energy cascade model ⋮ Dynamical fractional and multifractal fields ⋮ Growth of Sobolev norms in linear Schrödinger equations as a dispersive phenomenon ⋮ Dynamics of resonances for 0th order pseudodifferential operators

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