Author | Schapira, Pierre. author |
---|---|
Title | Microdifferential Systems in the Complex Domain [electronic resource] / by Pierre Schapira |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1985 |
Connect to | http://dx.doi.org/10.1007/978-3-642-61665-5 |
Descript | X, 216 p. online resource |
I. Microdifferential Operators -- Summary -- ยง 1. Construction of the Ring ?x -- Exercises -- ยง 2. Division Theorems -- Exercises -- ยง 3. Refined Microdifferential Cauchy-Kowalewski Theorem -- Exercises -- ยง 4. Microdifferential Modules Associated to a Submanifold -- Exercises -- ยง 5. Quantized Contact Transformations -- Exercises -- ยง 6. Systems with Simple Characteristics -- Exercises -- Notes -- II. ?X-modules -- Summary -- ยง 1. Filtered Rings and Modules -- Exercises -- ยง 2. Structure of the Ring ?X -- Exercises -- ยง 3. Operations on ?X-modules -- Exercises -- Notes -- III. Cauchy Problem and Propagation -- Summary -- ยง 1. Microcharacteristic Varieties -- Exercises -- ยง 2. The Cauchy Problem -- ยง 3. Propagation -- Exercises -- ยง 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