Computability in Analysis and Physics

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.

Marian B. Pour-El works in the School of Mathematics at the University of Minnesota.
J. Ian Richards works in the School of Mathematics at the University of Minnesota.