Computability and noncomputability in classical analysis
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 by Marian Boykan PourEl and Ian Richards PDF
 Trans. Amer. Math. Soc. 275 (1983), 539560 Request permission
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.References

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Additional Information
 © Copyright 1983 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 275 (1983), 539560
 MSC: Primary 03D80; Secondary 03F60, 26E05, 42A20, 47A99
 DOI: https://doi.org/10.1090/S00029947198306827171
 MathSciNet review: 682717