Distributions, Fourier Transforms And Some Of Their Applications To Physics

Download or read book Distributions, Fourier Transforms And Some Of Their Applications To Physics written by Thomas Schucker and published by World Scientific Publishing Company. This book was released on 1991-04-22 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, distributions are introduced via sequences of functions. This approach due to Temple has two virtues: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.