Damped Oscillatory Integral Operators with Analytic Phases
Damped Oscillatory Integral Operators with Analytic Phases
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DOI：
10.1006/aima.1997.1704
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发表时间：
1998-03
影响因子：
1.7
通讯作者：
D. H. Phong;E. Stein
中科院分区：
文献类型：
--
作者：
D. H. Phong;E. Stein
具有退化相函数的振荡积分算子的研究近年来引起了人们极大的兴趣。虽然一般的高维问题似乎遥不可及，在目前的情况下，已经取得了很大的进展，在一维的情况。在这种情况下，现在已知通常的振荡积分算子的衰减率由相位的约化牛顿图精确地确定（在解析情况下）。一个有趣的问题，仍然是相应的衰减率的“阻尼”振荡积分算子，特别是临界阻尼指数的值。本文旨在解决这一问题。我们开始回顾[5]的结果，其主要目标是研究具有任意高退化度的解析相位的振荡积分算子。设T* 是以下形式的算子：
The study of oscillatory integral operators with degenerate phase functions has attracted considerable interest lately. While the general higher dimensional problem seems out of reach at the present, much progress has been made in the one-dimensional situation. In this case, it is now known that the decay rate for the usual oscillatory integral operator is determined exactly by the reduced Newton diagram of the phase (in the analytic case). An intriguing issue that remained is the corresponding decay rate for the``damped''oscillatory integral operator and in particular the value of the critical damping exponent. The purpose of this paper is to solve this problem. We begin by recalling the results of [5], the main goal of which was the study of oscillatory integral operators with analytic phases of arbitrarily high degrees of degeneracy. Let T* be an operator of the form