Distributions Theory and Applications /

• Main Authors: Duistermaat, J.J (Author), Kolk, J.A.C (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston : Birkhäuser Boston, 2010.
• Edition: 1.
• Series: Cornerstones
• Subjects: Mathematics.; Approximation theory.; Fourier analysis.; Functional analysis.; Differential equations.; Partial differential equations.; Applied mathematics.; Engineering mathematics.; Functional Analysis.; Approximations and Expansions.; Applications of Mathematics.; Partial Differential Equations.; Fourier Analysis.; Ordinary Differential Equations.

This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quan...

Table of Contents:

• Motivation
• Test Functions
• Distributions
• Differentiation of Distributions
• Convergence of Distributions
• Taylor Expansion in Several Variables
• Localization
• Distributions with Compact Support
• Multiplication by Functions
• Transposition: Pullback and Pushforward
• Convolution of Distributions
• Fundamental Solutions
• Fractional Integration and Differentiation
• Fourier Transform
• Distribution Kernels
• Fourier Series
• Fundamental Solutions and Fourier Transform
• Supports and Fourier Transform
• Sobolev Spaces
• Appendix: Integration
• Solutions to Selected Problems.