Wave Front Set of Solutions to Sums of Squares of Vector Fields.

Intro -- Contents -- Abstract -- Chapter 1. Introduction -- Chapter 2. The Poisson-Treves Stratification -- 2.1. Analytic Stratification of an Analytic Set -- 2.2. Symplectic Stratification of an Analytic Submanifold -- 2.3. Poisson Stratification -- 2.4. Poisson Stratification Associated to Vector Fields -- Chapter 3. Standard Forms for a System of Vector Fields -- 3.1. The Symplectic Case of Depth &gt -- 1 -- 3.2. The Symplectic Case of Depth 1 -- 3.3. The Nonsymplectic Case of Depth &gt -- 1 -- 3.4. The Nonsymplectic Case of Depth 1 -- Chapter 4. Nested Strata -- Chapter 5. Bargman Pseudodifferential Operators -- 5.1. The FBI Transform -- 5.2. Pseudodifferential Operators -- 5.3. Some Pseudodifferential Calculus -- Chapter 6. The "A Priori" Estimate on the FBI Side -- 6.1. Proof of Theorem 6.1 -- 6.2. First Part of the Estimate: Estimate from Below -- 6.3. Second Part of the Estimate: Estimate from Above -- Chapter 7. A Single Symplectic Stratum -- 7.1. Σ=2 and ₁,…, _{ } Quasi-homogeneous -- 7.2. Σ&gt -- 2 -- 7.3. One Symplectic Stratum of Depth 1 -- Chapter 8. A Single Nonsymplectic Stratum -- 8.1. The Case _{\ | ℎ ( )}=2 and ᵢ Quasi-homogeneous -- 8.2. The Transversally Elliptic Case -- 8.3. A Class of Nontransversally Elliptic Operators -- Chapter 9. Microlocal Regularity in Nested Strata -- 9.1. Symplectic Stratifications -- 9.2. A Case of Nonsymplectic Stratification -- 9.3. A Case of Two Strata -- Chapter 10. Known Cases and Examples -- 10.1. The Case of Σ=2 -- 10.2. Okaji's Theorem -- Appendix A. A Bracket Lemma -- Appendix B. Nonsymplectic Strata Do Not Have the Reproducing Bracket Property -- Bibliography -- Index.

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