Analogue of Maslov’s Canonical Operator for Localized Functions and Its Applications to the Description of Rapidly Decaying Asymptotic Solutions of Hyperbolic Equations and Systems

An analogue of Maslov’s canonical operator for rapidly decaying functions is defined. The construction generalizes the ∂/∂τ-canonical operator on homogeneous manifolds from distributions to smooth localized functions. The main novelty is that the wave profile must be specified explicitly.