Methods and Applications of Analysis

Volume 18 (2011)

Number 2

Exponential decay for products of Fourier integral operators

Pages: 165 – 182



Nalini Anantharaman (Laboratoire de Mathématique, Université d’Orsay Paris XI, Orsay, France)


This text contains an alternative presentation, and in certain cases an improvement, of the “hyperbolic dispersive estimate” proved in [1, 3], where it was used to make progress towards the quantum unique ergodicity conjecture. The main statement gives a sufficient condition to have exponential decay of the norms of long products of sub-unitary Fourier integral operators. The improved version presented here is needed in the two papers [5] and [6].


semiclassical analysis, Fourier integral operators

2010 Mathematics Subject Classification

35S30, 58J40

Published 23 September 2011