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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Computability and noncomputability in classical analysis

Authors: Marian Boykan Pour-El and Ian Richards
Journal: Trans. Amer. Math. Soc. 275 (1983), 539-560
MSC: Primary 03D80; Secondary 03F60, 26E05, 42A20, 47A99
MathSciNet review: 682717
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Abstract: This paper treats in a systematic way the following question: which basic constructions in real and complex analysis lead from the computable to the noncomputable, and which do not? The topics treated include: computability for ${C^n}$, ${C^\infty }$, real analytic functions, Fourier series, and Fourier transforms. A final section presents a more general approach via "translation invariant operators". Particular attention is paid to those processes which occur in physical applications. The approach to computability is via the standard notion of recursive function from mathematical logic.

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Article copyright: © Copyright 1983 American Mathematical Society