Eigenfunction decay estimates in the quantum integrable case (Q1974819)

The paper under review is divided into 4 sections. Section 1 is a short introduction. Section 2 gives a microlocal weighted \( L ^2\)-estimate for the FBI transform of the joint eigenfunctions of \( n \) pair-wise-commuting \( \hbar \) analytic pseudodifferential operators. Section 3 gives two slightly different intrinsic constructions of the microlocal weight function. Finally, Section 4 derives decay estimates, as well as pointwise bounds for the joint eigenfunctions. These estimates are new and can be applied to a large variety of classical examples. Indeed a nice work.