Regularity theory of Fourier integral operators with complex phases and singularities of affine fibrations 1st Edition by Michael Ruzhansky ISBN 9061965039 by Michael Ruzhansky 9789061965039, 9061965039 instant download after payment.

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Product details:

ISBN 10: 9061965039 
ISBN 13: 9789061965039
Author: Michael Ruzhansky

Fourier integral operators (msc 35S30), Local singularities (msc 32S05), Singularities of holomorphic vector fields and foliations (msc 32S65), Smoothness and regularity of solutions (msc 35B65), Initial value problems for higher-order hyperbolic equations (msc 35L30), Initial value problems for pseudodifferential operators (msc 35S10), Pseudodifferential and Fourier integral operators on manifolds (msc 58J40)

Regularity theory of Fourier integral operators with complex phases and singularities of affine fibrations 1st Table of contents:

1. Fourier Integral Operators

1.1. Fourier Integral Operators with Real Phases
1.2. Fourier Integral Operators with Complex Phases
1.3. Spaces of Functions
1.4. Overview of the Regularity Theory for the Real Phase
1.5. Smooth Factorization Condition
  1.5.1. Smooth Factorization Condition
  1.5.2. Parametric Fibrations
  1.5.3. Operators Commuting with Translations
1.6. Fourier Integral Operators with Complex Phase Functions
1.7. Estimates for Operators with Complex Phases
1.8. A Relation Between Real and Complex Phases
1.9. Proofs
1.10. Estimates in Other Spaces
1.11. Essentially Homogeneous Case
  1.11.1. Essentially Homogeneous Case
  1.11.2. A Representation Formula for Continuous Operators of Small Negative Orders
1.12. Smooth Factorization Condition for Complex Phases

2. Affine and Jacobian Fibrations

2.1. Introduction
2.2. Affine Fibrations Setting
  2.2.1. Affine Fibrations Setting
  2.2.2. Jacobian Affine Fibrations Setting
2.3. Jacobian Affine Fibration Setting (continued)
2.4. Main Results
2.5. Methods of Complex Analytic Geometry
2.6. Some Properties of Affine Parametric Fibrations
2.7. General Properties of Affine Fibrations
2.8. Affine Fibrations of Jacobian Type
2.9. Limiting Properties of the Fibers

3. Fibrations and Phase Functions

3.1. Fibrations in Local Coordinates
3.2. Fibrations of Gradient Type
3.3. Reconstruction of the Phase Function
3.4. Existence of Singular Fibrations of Gradient Type

4. Analytic Aspects of Fourier Integral Operators

4.1. Complexification
4.2. Estimates for Analytic Fourier Integral Operators

5. Applications to Partial Differential Equations

5.1. Introduction
5.2. Cauchy Problem for a Class of Strictly Hyperbolic Equations
5.3. Monge–Ampère Equation
5.4. Cauchy Problems with Complex Characteristic Roots

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Tags: Michael Ruzhansky, Regularity, Fourier