Chapter 3: Functional analysis background
Abstract
In this chapter, we discuss the core background material on functional analysis and Hilbert space theory needed in the rest of the book. In Sections 3.1, 3.2, and 3.3 we present some basic concepts regarding normed vector spaces and Hilbert spaces. Then, in Section 3.4, we briefly discuss some classes of linear transformations that occur commonly in our study of infinite-dimensional deterministic and Bayesian inverse problems. The presentation here is brief. Throughout, we list a number of references for details on the topics discussed. Additional recommendations for further reading can be found in Section 3.5.
Fields of Study & Subjects
Advanced Banach Space Theory
Numerical methods in inverse problems
Optimization and Variational Analysis
Publication details
- Journal / source
- Society for Industrial and Applied Mathematics eBooks
- Pages
- 27–43
- Publication date
- 27 February 2026
- Language
- EN
- Document type
- Book chapter