Microdifferential Systems in the Complex Domain

Contents......Page all_7323_to_00224.cpc0007.djvu
Introduction......Page all_7323_to_00224.cpc0011.djvu
Summary......Page all_7323_to_00224.cpc0015.djvu
1.1. Differential Operators......Page all_7323_to_00224.cpc0016.djvu
1.2. Formal Microdifferential Operators......Page all_7323_to_00224.cpc0019.djvu
1.3. Microdifferential Operators......Page all_7323_to_00224.cpc0021.djvu
Exercises......Page all_7323_to_00224.cpc0023.djvu
2.1. A Banach Algebra of Operators......Page all_7323_to_00224.cpc0024.djvu
2.2. The Späth and Weierstrass Theorems......Page all_7323_to_00224.cpc0026.djvu
Exercises......Page all_7323_to_00224.cpc0029.djvu
3.1. Statement of the Theorem......Page all_7323_to_00224.cpc0030.djvu
3.2. The Abstract Cauchy-Kowalewski Theorem in Scales of Banach Spaces......Page all_7323_to_00224.cpc0032.djvu
3.3. Proof of Theorem 3.1.1......Page all_7323_to_00224.cpc0034.djvu
Exercises......Page all_7323_to_00224.cpc0035.djvu
4.1. The Sheaf C_{Z|X}......Page all_7323_to_00224.cpc0036.djvu
4.2. The Case when Z is a Hypersurface......Page all_7323_to_00224.cpc0040.djvu
4.3. The Sheaf E_{Y \rightarrow X}......Page all_7323_to_00224.cpc0042.djvu
Exercises......Page all_7323_to_00224.cpc0043.djvu
5.1. Division by an Ideal......Page all_7323_to_00224.cpc0044.djvu
5.2. Adjoint......Page all_7323_to_00224.cpc0046.djvu
5.3. Quantized Contact Transformations......Page all_7323_to_00224.cpc0047.djvu
5.4. Examples......Page all_7323_to_00224.cpc0049.djvu
Exercises......Page all_7323_to_00224.cpc0051.djvu
6.1. Equivalence of Operators......Page all_7323_to_00224.cpc0053.djvu
6.2. The Regular Involutive Case......Page all_7323_to_00224.cpc0054.djvu
6.3. Holonomic Systems with Simple Characteristics......Page all_7323_to_00224.cpc0056.djvu
Exercises......Page all_7323_to_00224.cpc0057.djvu
Notes......Page all_7323_to_00224.cpc0058.djvu
Summary......Page all_7323_to_00224.cpc0060.djvu
1.1. Noetherian and Zariskian Filtrations......Page all_7323_to_00224.cpc0061.djvu
1.2. Homological Properties......Page all_7323_to_00224.cpc0068.djvu
1.3. Characteristic Ideal......Page all_7323_to_00224.cpc0071.djvu
1.4. Sheaves of Filtered Modules......Page all_7323_to_00224.cpc0075.djvu
1.5. Examples......Page all_7323_to_00224.cpc0079.djvu
Exercises......Page all_7323_to_00224.cpc0081.djvu
2.1. The Ring E_X(0)......Page all_7323_to_00224.cpc0082.djvu
2.2. Main Properties of E_X......Page all_7323_to_00224.cpc0086.djvu
2.3. Characteristic Cycle......Page all_7323_to_00224.cpc0089.djvu
2.4. Holonomic Modules......Page all_7323_to_00224.cpc0091.djvu
2.5. Adjunction of a Dummy Variable......Page all_7323_to_00224.cpc0094.djvu
2.6. D_X-modules......Page all_7323_to_00224.cpc0096.djvu
Exercises......Page all_7323_to_00224.cpc0098.djvu
3.1. Definitions......Page all_7323_to_00224.cpc0100.djvu
3.2. Operations on B_{S|X}......Page all_7323_to_00224.cpc0104.djvu
3.3. Operations on C_{S|X}......Page all_7323_to_00224.cpc0109.djvu
3.4. Operations on E_X-modules......Page all_7323_to_00224.cpc0112.djvu
3.5. Complement on Inverse Images......Page all_7323_to_00224.cpc0118.djvu
Exercises......Page all_7323_to_00224.cpc0121.djvu
Notes......Page all_7323_to_00224.cpc0122.djvu
Summary......Page all_7323_to_00224.cpc0124.djvu
1.1. Normal Cones......Page all_7323_to_00224.cpc0126.djvu
1.2. 1-microcharacteristic Variety......Page all_7323_to_00224.cpc0129.djvu
1.3. Characteristic Varieties Associated to a Submersion......Page all_7323_to_00224.cpc0134.djvu
1.4. Characteristic Varieties Associated to an Embedding......Page all_7323_to_00224.cpc0137.djvu
1.5. Characteristic Variety of the Systems Induced on a Submanifold......Page all_7323_to_00224.cpc0140.djvu
1.6. Coherency of the Systems Induced on a Submanifold......Page all_7323_to_00224.cpc0143.djvu
Exercises......Page all_7323_to_00224.cpc0146.djvu
2.1. The Cauchy Problem for a System......Page all_7323_to_00224.cpc0147.djvu
2.2. Application: The Cauchy Problem with Data Ramified along Hypersurfaces......Page all_7323_to_00224.cpc0153.djvu
Exercises......Page all_7323_to_00224.cpc0157.djvu
3.1. Propagation at the Boundary for one Operator......Page all_7323_to_00224.cpc0158.djvu
3.2. Propagation for Systems......Page all_7323_to_00224.cpc0165.djvu
Exercises......Page all_7323_to_00224.cpc0167.djvu
4.1. Real and Complex Stratifications......Page all_7323_to_00224.cpc0168.djvu
4.2. Micro-support of Sheaves......Page all_7323_to_00224.cpc0173.djvu
4.3. Micro-supports and Microcharacteristic Varieties......Page all_7323_to_00224.cpc0175.djvu
Exercises......Page all_7323_to_00224.cpc0179.djvu
Notes......Page all_7323_to_00224.cpc0181.djvu
A.1. Symplectic Vector Spaces......Page all_7323_to_00224.cpc0183.djvu
A.2. Symplectic Manifolds......Page all_7323_to_00224.cpc0184.djvu
A.3. Homogeneous Symplectic Structures......Page all_7323_to_00224.cpc0185.djvu
A.4. Contact Transformations......Page all_7323_to_00224.cpc0186.djvu
B.1. Categories and Derived Functors......Page all_7323_to_00224.cpc0189.djvu
B.2. Rings and Modules......Page all_7323_to_00224.cpc0194.djvu
B.3. Graded Rings and Modules......Page all_7323_to_00224.cpc0196.djvu
B.4. Koszul Complexes......Page all_7323_to_00224.cpc0197.djvu
B.5. The Mittag-Leffler Condition......Page all_7323_to_00224.cpc0199.djvu
C.1. Presheaves and Sheaves......Page all_7323_to_00224.cpc0200.djvu
C.2. Cohomology of Sheaves......Page all_7323_to_00224.cpc0202.djvu
C.3. Čech Cohomology......Page all_7323_to_00224.cpc0204.djvu
C.4. An Extension Theorem......Page all_7323_to_00224.cpc0205.djvu
C.5. Coherent Sheaves......Page all_7323_to_00224.cpc0208.djvu
D.1. Support and Multiplicities......Page all_7323_to_00224.cpc0209.djvu
D.2. Homological Dimension......Page all_7323_to_00224.cpc0212.djvu
Bibliography......Page all_7323_to_00224.cpc0213.djvu
List of Notations and Conventions......Page all_7323_to_00224.cpc0217.djvu
Index......Page all_7323_to_00224.cpc0222.djvu