Fourier integral operators with complex-valued phase functions
Fourier integral operators with complex-valued phase functions
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DOI：
10.1007/bfb0074195
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发表时间：
1975
期刊：
影响因子：
--
通讯作者：
A. Melin;J. Sjöstrand
中科院分区：
文献类型：
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作者：
A. Melin;J. Sjöstrand
在本文中，我们将提出我们认为的 H~rmander 傅里叶积分算子理论对复值相位函数情况的自然延伸。当试图为具有非实主符号的主类型算子构造参数或奇异齐次解时，通常会出现复杂的相位函数，这是一个众所周知的现象。因此，需要为具有复值相位函数的傅里叶积分算子建立一个系统的理论。我们的论文很大程度上遵循 H~rmander 的文章~ 3]，我们假设读者熟悉这篇论文。我们还将使用与~3]中相同的符号来表示函数空间、符号等。让我们简短地描述一下在尝试推广这一理论时遇到的新困难之一。傅里叶积分分布（或简称傅里叶分布）应该是一个分布 A g~(~ n)，在适当的意义上，它由（微局部）给出
In this paper we shall present what we think is the natural extension of H~ rmander's theory of Fourier integral operators to the case of complex valued phase functions. it is a well known phenomenon that complex phase functions appear in general~ when one tries to construct parametrices or singular homogeneous solutions for operators of principal type with non-real principal symbol. lt is therefore desirable to dispose a systematic theory for Fourier integral operators with complex valued phase functions. Our paper follows very much the article~ 3] of H~ rmander and we shall assume that the reader is acquainted with this paper. We shall also use the same notations as in~ 3] for function spaces, symbols and so on. Let us shortly describe one of the new difficulties one meets when trying to generalize the theory. A Fourier integral distribution (or Fourier distribution for short) should be a distribution A g~(~ n) which in a suitable sense is given (microlocally) by