Symbols and Formal Symbols of Pseudodifferential Operators
Symbols and Formal Symbols of Pseudodifferential Operators
复制标题
伪微分算子的符号和形式符号
DOI：
10.2969/aspm/00410181
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发表时间：
1984
期刊：
影响因子：
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通讯作者：
T. Aoki
中科院分区：
文献类型：
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作者：
T. Aoki
用X = X'支撑的共束束上定义的圆锥形微功能核K（X，X'）。 $ r（[5]，[6]，[8]）表示假差异操作员的环的捆。从凯奇（Cauchy）的积分公式来看，$ r包含具有分析系数的所有线性差分运算符。此外，$ r包括微分算子的捆绑$ 00（[10]）。不用说，这些运营商在调查各种问题中非常重要。我们强调，这些类包含无限顺序的操作员，并且在许多情况下，使用此类操作员至关重要（参见[6]，[10]，[12]）。伪差算子的符号由Kataoka [7]定义。他借助ra的辅助转换来定义$ r的共同体定义的符号。另一方面，Boutet de Monvel [4]通过为给定符号类别使用振荡积分来引入分析伪差异操作员，并表明标准符号积分有效，并且在COO类别中是有效的（例如，请参见[11]）。我们注意到，从[4]的意义上讲，伪差的运算符凭借Kataoka的理论包含在8美元中。本文的目的是从[7]的角度发展和完成$ r的符号理论。观点的优点与$ r的共同体定义的不变性有关。捆绑本身是独立于局部坐标系统的选择来定义的。定义$ r的共同体组可以用ra transformation的方法来表示（[7]，[8]）;我们将充分利用该方法。我们的主要贡献之一是介绍
with a holomorphic microfunction kernel K(x, x') defined on the conormal bundle supported by x=x'. The sheaf of rings of pseudodifferential operators is denoted by $R ([5], [6], [8]). It follows from Cauchy's integral formula that $R contains all linear differential operators with analytic coefficients. Moreover, $R includes the sheaf $00 of microdifferential operators ([10]). Needless to say, those classes of operators are very important in the investigations of various problems. We emphasize that the classes contain operators of infinite order and that the use of such operators is crucial in many cases (cf. [6], [10], [12]). Symbols of pseudodifferential operators are defined by Kataoka [7]. He defines symbols from the cohomological definition of $R by the aid of Radon transformations. On the other hand, Boutet de Monvel [4] introduces analytic pseudodifferential operators by using oscillatory integrals for given symbol classes and shows that standard symbolic calculus is valid as well as in Coo-category (see [11], for example). We note that pseudodifferential operators in the sense of [4] are contained in $8 by virtue of Kataoka's theory. The aim of this paper is to develop and to complete the symbol theory of $R from the standpoint of [7]. The advantages of the viewpoint are related to the invariance of the cohomological definition of $R. The sheaf itself is defined independently of a choice of local coordinate systems. The cohomology group which defines $R can be represented elementarily by the method of the Radon transformation ([7], [8]); we shall make full use of the method. One of our main contributions is introducing the
（偏）微分算子的中间卷积
DOI：
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发表时间：
2009
期刊：
影响因子：
--
作者：
Kentaroh Watanabe;Kensuke Wada;Hidehiro Kaneda;Kensuke Ide;Masahiro Kato;Takehiko Wada;K. Ishige and T. Kawakami;平沢和司;水谷勉・尾崎久記・小池敏英;Nariya Kawazumi;大島利雄
通讯作者：
大島利雄