Residues and Hyperfunctions
Residues and Hyperfunctions
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残留和功能亢进
DOI：
10.1007/978-3-030-95760-5_8
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Tatsuo Suwa
中科院分区：
文献类型：
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作者：
Cho Jong Taek;Kimura Makoto;Tatsuo Suwa
我们讨论了相对的捷克-德拉姆上同调和相对的捷克-多尔博特上同调及其应用。在德拉姆的情况下，我们主要关注的是通过亚历山大对偶局部化特征类而产生的剩余。相对的Čech-de Rham定理允许我们从拓扑和微分几何的观点来处理这个问题，并且两者的比较产生了各种有趣的剩余表达式和应用。在Dolbeault情形中，相对的Čech-Dolbeault上同调与全纯形式层的相对上同调是正则同构的。作为应用，我们给出了Sato超函数及其相关运算的显式表达式，包括将真实的解析函数空间嵌入到超函数空间中，其中Thom类也起着重要的作用.
We discuss relative Čech-de Rham and relative Čech-Dolbeault cohomologies and their applications. In the de Rham case, we are mainly concerned with the residues that arise from the localization of characteristic classes via the Alexander duality. The relative Čech-de Rham theorem allows us to deal with the problem from both the topological and differential geometric viewpoints and the comparison of the two yields various interesting expressions of the residues and applications. In the Dolbeault case, the relative Čech-Dolbeault cohomology turns out to be canonically isomorphic with the relative cohomology of the sheaf of holomorphic forms. As an application, we give explicit expressions of Sato hyperfunctions and related operations including the embedding of the space of real analytic functions into that of hyperfunctions, where as well the Thom class plays an important role.