Microdifferential Systems in the Complex Domain / by Pierre Schapira
(Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics ; 269)
| データ種別 | 電子ブック |
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| 出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg |
| 出版年 | 1985 |
| 本文言語 | 英語 |
| 大きさ | X, 216 p : online resource |
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| 内容注記 | I. Microdifferential Operators Summary § 1. Construction of the Ring ?x Exercises § 2. Division Theorems Exercises § 3. Refined Microdifferential Cauchy-Kowalewski Theorem Exercises § 4. Microdifferential Modules Associated to a Submanifold Exercises § 5. Quantized Contact Transformations Exercises § 6. Systems with Simple Characteristics Exercises Notes II. ?X-modules Summary § 1. Filtered Rings and Modules Exercises § 2. Structure of the Ring ?X Exercises § 3. Operations on ?X-modules Exercises Notes III. Cauchy Problem and Propagation Summary § 1. Microcharacteristic Varieties Exercises § 2. The Cauchy Problem § 3. Propagation Exercises § 4. Constructibility Exercises Notes Appendices A. Symplectic Geometry A.1. Symplectic Vector Spaces A.2. Symplectic Manifolds A.3. Homogeneous Symplectic Structures A.4. Contact Transformations B. Homological Algebra B.1. Categories and Derived Functors B.2. Rings and Modules B.3. Graded Rings and Modules B.4 Koszul Complexes B.5. The Mittag-Leffler Condition C. Sheaves C.1. Presheaves and Sheaves C.2. Cohomology of Sheaves C.3. ?ech Cohomology C.4. An Extension Theorem C.5. Coherent Sheaves D.1. Support and Multiplicities D.2. Homological Dimension List of Notations and Conversions |
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| 一般注記 | The words "microdifferential systems in the complex domain" refer to seve ral branches of mathematics: micro local analysis, linear partial differential equations, algebra, and complex analysis. The microlocal point of view first appeared in the study of propagation of singularities of differential equations, and is spreading now to other fields of mathematics such as algebraic geometry or algebraic topology. How ever it seems that many analysts neglect very elementary tools of algebra, which forces them to confine themselves to the study of a single equation or particular square matrices, or to carryon heavy and non-intrinsic formula tions when studying more general systems. On the other hand, many alge braists ignore everything about partial differential equations, such as for example the "Cauchy problem", although it is a very natural and geometri cal setting of "inverse image". Our aim will be to present to the analyst the algebraic methods which naturally appear in such problems, and to make available to the algebraist some topics from the theory of partial differential equations stressing its geometrical aspects. Keeping this goal in mind, one can only remain at an elementary level |
| 著者標目 | *Schapira, Pierre author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Algebraic geometry LCSH:Category theory (Mathematics) LCSH:Homological algebra FREE:Mathematics FREE:Category Theory, Homological Algebra FREE:Algebraic Geometry |
| 分 類 | DC23:512.6 |
| 巻冊次 | ISBN:9783642616655 
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| ISBN | 9783642616655 |
| URL | http://dx.doi.org/10.1007/978-3-642-61665-5 |
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