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Computability in Analysis and Physics

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This book represents the first treatment of computable analysis at the graduate level within the tradition of classical mathematical reasoning. Among the topics dealt with are: classical analysis, Hilbert and Banach spaces, bounded and unbounded linear operators, eigenvalues, eigenvectors, and equations of mathematical physics. The book is self-contained, and yet sufficiently detailed to provide an introduction to research in this area.

Author(s): Marian Boykan Pour-El, J. Ian Richards
Series: Perspectives in Mathematical Logic
Publisher: Springer
Year: 1989

Language: English
Pages: 212


Content:
Front Matter....Pages I-XI
Introduction....Pages 1-5
Prerequisites from Logic and Analysis....Pages 6-8
Front Matter....Pages 9-9
An Introduction to Computable Analysis....Pages 11-49
Further Topics in Computable Analysis....Pages 50-73
Front Matter....Pages 75-75
Computability Structures on a Banach Space....Pages 77-92
The First Main Theorem and Its Applications....Pages 93-120
Front Matter....Pages 121-121
The Second Main Theorem, the Eigenvector Theorem, and Related Results....Pages 123-148
Proof of the Second Main Theorem....Pages 149-191
Addendum: Open Problems....Pages 192-194
Back Matter....Pages 195-206