Topological Vector Spaces and Distributions - (Dover Books on Mathematics) by John Horvath (Paperback)

About the Book

Precise exposition provides an excellent summary of the modern theory of locally convex spaces and develops the theory of distributions in terms of convolutions, tensor products, and Fourier transforms. 1966 edition.

Book Synopsis

"The most readable introduction to the theory of vector spaces available in English and possibly any other language."--J. L. B. Cooper, MathSciNet Review
Mathematically rigorous but user-friendly, this classic treatise discusses major modern contributions to the field of topological vector spaces. The self-contained treatment includes complete proofs for all necessary results from algebra and topology. Suitable for undergraduate mathematics majors with a background in advanced calculus, this volume will also assist professional mathematicians, physicists, and engineers.
The precise exposition of the first three chapters--covering Banach spaces, locally convex spaces, and duality--provides an excellent summary of the modern theory of locally convex spaces. The fourth and final chapter develops the theory of distributions in relation to convolutions, tensor products, and Fourier transforms. Augmented with many examples and exercises, the text includes an extensive bibliography.

About the Author

John Horvath is Professor Emeritus of Mathematics at the University of Maryland in College Park.