Distributions Theory and Applications /

• Main Authors: Duistermaat, J.J. (Author), Kolk, J.A.C. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Boston : Birkhũser Boston, 2010.
• Edition: 1.
• Series: Cornerstones
• Subjects: Mathematics.; Fourier analysis.; Differential Equations.; Differential equations, partial.; Approximations and Expansions.; Applications of Mathematics.; Partial Differential Equations.; Fourier Analysis.; Ordinary Differential Equations.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-8176-4675-2

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:

• Preface
• 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 Push forward
• Convolution of Distributions
• Fundamental Solutions
• Fractional Integration and Differentiation
• Fourier Transformation
• Fourier Series
• Fundamental Solutions and Fourier Transformation
• Supports and Fourier Transformation
• Sobolev Spaces
• Appendix: Results from Measure Theory in the Context of Distributions
• Examination Exercises with Solutions
• Solutions to Selected Exercises
• References
• Index.