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In this book, distributions are introduced via sequences of functions. This approach due to Temple has two virtues:
- It only presupposes standard calculus.
- It allows to justify manipulations necessary in physical applications.
The Fourier transform is defined for functions and generalized to distributions, while the Green function is defined as the outstanding application of distributions. Using Fourier transforms, the Green functions of the important linear differential equations in physics are computed. Linear algebra is reviewed with emphasis on Hilbert spaces. The author explains how linear differential operators and Fourier transforms naturally fit into this frame, a point of view that leads straight to generalized fourier transforms and systems of special functions like spherical harmonics, Hermite, Laguerre, and Bessel functions.
Sample Chapter(s)
Chapter 1: Functions of a complex variable (522 KB)
Contents:
- Functions of a Complex Variable
- Distributions
- Fourier Series
- Fourier Transforms
- Some Linear Differential Operators and their Green Functions
- Linear Algebra in Infinite Dimensions
- Systems of Special Functions
Readership: Physicists, mathematicians, engineers and undergraduates.
