#### Vol. 1, No. 3, 2019

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Microlocal analysis of forced waves

### Semyon Dyatlov and Maciej Zworski

Vol. 1 (2019), No. 3, 359–384
##### Abstract

We use radial estimates for pseudodifferential operators to describe long-time evolution of solutions to $i{u}_{t}-Pu=f$, where $P$ is a self-adjoint zeroth-order pseudodifferential operator satisfying hyperbolic dynamical assumptions and where $f$ is smooth. This is motivated by recent results of Colin de Verdière and Saint-Raymond (2019) concerning a microlocal model of internal waves in stratified fluids.

 Dedicated to Richard Melrose on the occasion of his 70th birthday
##### Keywords
forced waves, spectral theory, pseudodifferential operators, radial estimates
Primary: 35A27