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Available5.0
38 reviews
ISBN 10: 3764385111
ISBN 13: 9783764385118
Author: Fabio Nicola, Luigi Rodino
Part I: Preliminaries and Basic Calculus
Chapter 1: Pseudo-differential Operators: Definitions and Basic Properties
1.1 Introduction: From Differential to Pseudo-differential Operators
1.2 Symbol Classes
1.3 Quantization of Operators
1.4 Adjoint and Transposed Operators
1.5 Composition of Operators
1.6 Global Ellipticity and Hypoellipticity
1.7 Parametrices and Regularity
Chapter 2: Function Spaces and Fourier Analysis
2.1 Schwartz Space and Tempered Distributions
2.2 Fourier Transform
2.3 Sobolev Spaces (Basic Introduction)
2.4 Weighted Function Spaces
Chapter 3: Further Properties of Pseudo-differential Operators
3.1 Boundedness on L2 and other function spaces
3.2 Global Regularity Properties
3.3 Pseudo-differential Operators with Slowly Varying Symbols
Part II: Advanced Topics and Applications
Chapter 4: Special Classes of Pseudo-differential Operators
4.1 Weyl Calculus
4.2 Pseudo-differential Operators of Non-integer Order
4.3 Pseudo-differential Operators with Non-smooth Symbols
Chapter 5: Global Hypoellipticity
5.1 Introduction to Global Hypoellipticity
5.2 Conditions for Global Hypoellipticity
5.3 Examples and Applications
Chapter 6: Applications to Partial Differential Equations
6.1 Elliptic Equations
6.2 Evolution Equations (Parabolic, Hyperbolic - often discussed in the context of global solutions)
6.3 Schrödinger Type Operators
6.4 Traveling Wave Equations
Chapter 7: Applications in Mathematical Physics and Quantum Mechanics
7.1 Quantum Mechanics (e.g., phase space analysis, quantization)
7.2 Signal Analysis
Chapter 8: Non-commutative Geometry Aspects (if applicable to the global context of the book)
(This chapter might explore connections between pseudo-differential operators and non-commutative spaces or algebras.)
pseudo-differential calculus
calculus global edition 2nd edition
global pseudo-differential calculus on euclidean spaces
global differential geometry
global divergence theorems in nonlinear pdes and geometry
Tags: Fabio Nicola, Luigi Rodino, Global, Pseud
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