Foundation of symbol theory for analytic pseudodifferential operators(1)
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- Aoki Takashi
- Department of Mathematics, Kindai University
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- Honda Naofumi
- Department of Mathematics, Faculty of Science, Hokkaido University
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- Yamazaki Susumu
- Department of General Education, College of Science and Technology, Nihon University
書誌事項
- タイトル別名
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- Foundation of symbol theory for analytic pseudodifferential operators, I
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<p>A new symbol theory for pseudodifferential operators in the complex analytic category is given. Here the pseudodifferential operators mean integral operators with real holomorphic microfunction kernels. The notion of real holomorphic microfunctions had been introduced by Sato, Kawai and Kashiwara by using sheaf cohomology theory. Symbol theory for those operators was partly developed by Kataoka and by the first author and it has been effectively used in the analysis of operators of infinite order. However, there was a missing part that links the symbol theory and the cohomological definition of operators, that is, the consistency of the Leibniz–Hörmander rule and the cohomological definition of composition for operators. This link has not been established completely in the existing symbol theory. This paper supplies the link and provides a cohomological foundation of the symbolic calculus of pseudodifferential operators.</p>
収録刊行物
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 69 (4), 1715-1801, 2017
一般社団法人 日本数学会
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詳細情報 詳細情報について
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- CRID
- 1390282680091611648
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- NII論文ID
- 130006887116
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- NII書誌ID
- AA0070177X
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- ISSN
- 18811167
- 18812333
- 00255645
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- NDL書誌ID
- 028590696
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- NDL
- Crossref
- CiNii Articles
- KAKEN
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- 使用不可