Distributions, Partial Differential Equations, and Harmonic Analysis

• Main Author: Mitrea, Dorina. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2013.
• Series: Universitext,
• Subjects: Mathematics.; Fourier analysis.; Functional analysis.; Differential equations, partial.; Potential theory (Mathematics).; Partial Differential Equations.; Functional Analysis.; Fourier Analysis.; Potential Theory.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-4614-8208-6

The aim of this book is to offer, in a concise, rigorous, and largely self-contained manner, a rapid introduction to the theory of distributions and its applications to partial differential equations and harmonic analysis. The book is written in a format suitable for a graduate course spanning eithe...

Table of Contents:

• Introduction
• Summary of Topological and Functional Analysis Results
• Weak Derivatives
• The Space D0() of Distributions
• The Fourier Transform
• The Space of Tempered Distributions
• Fundamental Solution
• The Laplace Operator
• The Heat Operator
• The Wave Operator
• The Lame Operator
• Fundamental Solutions for Other Operators
• Hypoelliptic operators
• Sobolev spaces
• Appendix
• References.�.