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E-raamat: Wave Front Set of Solutions to Sums of Squares of Vector Fields

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Wave Front Set of Solutions to Sums of Squares of Vector FieldsSuurem pilt
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Italian mathematicians Albano (U. of Rome) and Bove (U. of Bologna) explore the (micro)hypoanalyticity and the Genrey hypoellipticity of sums of squares of vector fields in terms of the Poisson-Treves stratification. Using the Fourier Bros Iagolnitzer (FBI) transform, they demonstrate hypoanalyticity for several classes of sums of squares, and show that though their method is not general, it includes almost every known hypoanalyticity result. There is no index. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com)
Chapter 1 Introduction
vii
Chapter 2 The Poisson-Treves Stratification
1(6)
2.1 Analytic Stratification of an Analytic Set
1(1)
2.2 Symplectic Stratification of an Analytic Submanifold
2(2)
2.3 Poisson Stratification
4(1)
2.4 Poisson Stratification Associated to Vector Fields
5(2)
Chapter 3 Standard Forms for a System of Vector Fields
7(20)
3.1 The Symplectic Case of Depth >1
7(3)
3.2 The Symplectic Case of Depth > 1
10(6)
3.3 The Nonsymplectic Case of Depth > 1
16(3)
3.4 The Nonsymplectic Case of Depth 1
19(8)
Chapter 4 Nested Strata
27(2)
Chapter 5 Bargman Pseudodifferential Operators
29(4)
5.1 The FBI Transform
29(1)
5.2 Pseudodifferential Operators
30(1)
5.3 Some Pseudodifferential Calculus
31(2)
Chapter 6 The "A Priori" Estimate on the FBI Side
33(8)
6.1 Proof of Theorem 6.1
34(1)
6.2 First Part of the Estimate: Estimate from Below
34(1)
6.3 Second Part of the Estimate: Estimate from Above
35(6)
Chapter 7 A Single Symplectic Stratum
41(10)
7.1 Dim Σ = 2 and X1, ..., XN Quasi-homogeneous
44(2)
7.2 Codim Σ > 2
46(1)
7.3 One Symplectic Stratum of Depth 1
47(4)
Chapter 8 A Single Nonsymplectic Stratum
51(4)
8.1 The Case rank σChar(p) =2 and Xi Quasi-homogeneous
52(1)
8.2 The Transversally Elliptic Case
53(1)
8.3 A Class of Nontransversally Elliptic Operators
54(1)
Chapter 9 Microlocal Regularity in Nested Strata
55(6)
9.1 Symplectic Stratifications
55(2)
9.2 A Case of Nonsymplectic Stratification
57(3)
9.3 A Case of Two Strata
60(1)
Chapter 10 Known Cases and Examples
61(2)
10.1 The Case of codim Σ = 2
61(1)
10.2 Okaji's Theorem
62(1)
Appendix A A Bracket Lemma 63(6)
Appendix B Nonsymplectic Strata Do Not Have the Reproducing Bracket Property 69(2)
Bibliography 71(2)
Index 73
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