Semiclassical asymptotics for nonselfadjoint harmonic oscillators

The energy of solutions of the scalar damped wave equation decays uniformly exponentially fast when the geometric control condition is satisfied.. A theorem of Lebeau [Leb93] gives

a) We first study the case when ǫλ converges slowly to c.. , J } corresponds to a bounded spatial domain, and can be treated exactly as in ii) and iii). Thus is it sufficient

In Section 5, we provide a suitable version of the Mourre theory which allows to estimate powers of the resolvent, including inserted factors, for general dissipative perturbations

Four years ago, Pelayo, Polterovich and V˜ u Ngo.c proposed in [ 31] a minimal set of axioms that a collection of commuting semiclassical self-adjoint operators should satisfy in

K, Batty, R, Chill, S, Srivastava, Maximal regularity in interpo- lation spaces for second order Cauchy problems, Operator semigroups meet complex analysis, harmonic analysis

in general an algebraic decay and the convergence to the travelling fronts depends on the algebraic decay rate of the initial condition and exponentially decaying initial

Local energy decay, damped wave equation, Mourre’s commutators method, non- selfadjoint operators, resolvent