Generalized oscillatory integrals and Fourier integral operators
Generalized oscillatory integrals and Fourier integral operators
复制标题
广义振荡积分和傅立叶积分算子
DOI：
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发表时间：
2006
影响因子：
0.7
通讯作者：
M. Oberguggenberger
中科院分区：
文献类型：
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作者：
Claudia Garetto;G. Hörmann;M. Oberguggenberger
本文建立了一种广义振荡积分的理论，它的相函数和振幅可以是广义Colombeau型函数。在此基础上，定义了作用于Colombeau代数上的广义Fourier积分算子.这是出于需要一个一般框架的偏微分算子与非光滑系数和分布dataffi这些FIO的映射特性进行了研究，因为是微局部Colombeau正则性的OI和FIO行动的影响广义波前集。
Abstract In this paper, a theory is developed of generalized oscillatory integrals (OIs) whose phase functions and amplitudes may be generalized functions of Colombeau type. Based on this, generalized Fourier integral operators (FIOs) acting on Colombeau algebras are defined. This is motivated by the need for a general framework for partial differential operators with non-smooth coefficients and distribution dataffi The mapping properties of these FIOs are studied, as is microlocal Colombeau regularity for OIs and the influence of the FIO action on generalized wavefront sets.