Description
Book SynopsisIntroduces functional analysis to undergraduate mathematics students who possess a basic background in analysis and linear algebra. By studying how the Volterra operator acts on vector spaces of continuous functions, its readers will sharpen their skills, reinterpret what they already know, and learn fundamental Banach-space techniques.
Table of Contents
- From Volterra to Banach: Starting out
- Springing ahead
- Springing higher
- Operators as points
- Travels with Titchmarsh: The Titchmarsh convolution theorem
- Titchmarsh finale
- Invariance through duality: Invariant subspaces
- Digging into duality
- Rendezvous with Riez
- V-invariance: Finale
- Uniform convergence
- $\mathbb{C}$omplex primer
- Uniform approximation by polynomials
- Riemann-Stieltjes primer
- Bibliography
- Index
