On pointwise decay of waves

Abstract

This article serves as an introduction to the linear aspects of the recent submission by Krieger, Miao, and the author, see arXiv:2009.08843. It also surveys some of the results obtained on the decay of linear waves on various backgrounds or in the presence of a potential over the past 15 years. Particular emphasis is placed on the role of 0 energy. The techniques are based on spectral and scattering theory. Note that this is not a systematic review, as this would require a book.

This article is dedicated to the memory of Jean Bourgain. 5 figures are included. Revised version, to appear in Journal Math. Phys

References in corpus (3)

• Dispersive estimates for Schrodinger operators in dimensions one and three
• A counterexample to dispersive estimates for Schrödinger operators in higher dimensions
• A stability theory beyond the co-rotational setting for critical Wave Maps blow up

Cited by in corpus (4)

• Late-time asymptotics for geometric wave equations with inverse-square potentials
• Dispersive estimates for higher order Schrödinger operators with scaling-critical potentials
• The Massless Dirac Equation in Three Dimensions: Dispersive estimates and zero energy obstructions
• Price's law on Minkowski space in the presence of an inverse square potential