On the representation of localized functions in ℝ2 by the Maslov canonical operator

被引：0
|
作者：
V. E. Nazaikinskii
机构：
[1] Russian Academy of Sciences,Ishlinskii Institute for Problems in Mechanics
[2] Moscow Institute for Physics and Technology,undefined
来源：
Mathematical Notes | 2014年 / 96卷
关键词：
wave equation; asymptotics; localized initial data; integral representation; invariant Lagrangian manifold; the Maslov canonical operator;
D O I：
暂无
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学科分类号：
摘要：
We prove that localized functions can be represented in the form of an integral over a parameter, the integrand being the Maslov canonical operator applied to an amplitude obtained from the Fourier transform of the function to be represented. This representation generalizes an earlier one obtained by Dobrokhotov, Tirozzi, and Shafarevich and permits representing localized initial data for wave type equations with the use of an invariant Lagrangian manifold, which simplifies the asymptotic solution formulas dramatically in many cases.
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页码：99 / 109
页数：10
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