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

Corresponding Members of the RAS V. E. Nazaikinskii^a^,^b^,* and A. I. Shafarevich^a^,^b^,^c^,^d^,**
Translated by I. Ruzanova

^aIshlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia

^bMoscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow oblast, 141700 Russia

^c Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia

^dNational Research Center “Kurchatov Institute”, Moscow, 123182 Russia

Correspondence to: *e-mail: nazaikinskii@googlemail.com
Correspondence to: **e-mail: shafarev@yahoo.com

Received 9 January, 2018

Abstract—An analogue of Maslov’s canonical operator for rapidly decaying functions is defined. The construction generalizes the $\frac{\partial }{{\partial \tau }}$-canonical operator on homogeneous manifolds from distributions to smooth localized functions. The main novelty is that the wave profile must be specified explicitly.

DOI: 10.1134/S1064562418020217