Wave front set of solutions to sums of squares of vector fields / Paolo Albano, Antonio Bove.

Format:

Book

Author/Creator:

Albano, Paolo, 1969- author.

Bove, Antonio, author.

Series:

Memoirs of the American Mathematical Society ; Volume 221, Number 1039.

Memoirs of the American Mathematical Society, 1947-6221 ; Volume 221, Number 1039

Language:

English

Subjects (All):

Wavelets (Mathematics).

Summability theory.

Vector fields.

Physical Description:

1 online resource (73 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2012.

Language Note:

English

Summary:

The authors study the (micro)hypoanalyticity and the Gevrey hypoellipticity of sums of squares of vector fields in terms of the Poisson-Treves stratification. The FBI transform is used. They prove hypoanalyticity for several classes of sums of squares and show that their method, though not general, includes almost every known hypoanalyticity result. Examples are discussed.

Contents:

""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 >1""; ""3.2. The Symplectic Case of Depth 1""; ""3.3. The Nonsymplectic Case of Depth >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 Prioriâ€? 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 â??,â€?, _{ } Quasi-homogeneous""; ""7.2. Σ>2""; ""7.3. One Symplectic Stratum of Depth 1""; ""Chapter 8. A Single Nonsymplectic Stratum""

""Index""

Notes:

"January 2013, Volume 221, Number 1039 (third of 5 numbers)."

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-8218-9461-7