Computability in Analysis and Physics

The first graduate-level treatment of computable analysis within the tradition of classical mathematical reasoning.

Marian B. Pour-El (Author), J. Ian Richards (Author)

9781107168442, Cambridge University Press

Hardback, published 2 March 2017

218 pages, 5 b/w illus.
24.1 x 16.2 x 1.8 cm, 0.5 kg

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the first publication in the Perspectives in Logic series, Pour-El and Richards present the first graduate-level treatment of computable analysis within the tradition of classical mathematical reasoning. The book focuses on the computability or noncomputability of standard processes in analysis and physics. Topics include classical analysis, Hilbert and Banach spaces, bounded and unbounded linear operators, eigenvalues, eigenvectors, and equations of mathematical physics. The work is self-contained, and although it is intended primarily for logicians and analysts, it should also be of interest to researchers and graduate students in physics and computer science.

Introduction
Prerequisites from logic and analysis
Part I. Computability in Classical Analysis: An introduction to computable analysis
1. Further topics in computable analysis
Part II. The Computability Theory of Banach Spaces: 2. Computability structures on a Banach space
3. The first main theorem and its applications
Part III. The Computability Theory of Eigenvalues and Eigenvectors: 4. The second main theorem, the eigenvector theorem, and related results
5. Proof of the second main theorem
Addendum: open problems
Bibliography
Subject index.

Subject Areas: Mathematical theory of computation [UYA], Mathematical physics [PHU], Functional analysis & transforms [PBKF]