Undecidability through Fourier series
Peter Buser,Bruno Scarpellini +1 more
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TLDR
Production systems are introduced, viewed as counterparts of the combinatorial ones, that generate all recursively enumerable predicates in this way using as tools only elementary operations and functions from classical Analysis.About:
This article is published in Annals of Pure and Applied Logic.The article was published on 2016-07-01 and is currently open access. It has received 1 citations till now. The article focuses on the topics: Fourier inversion theorem & Fourier series.read more
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Computability and Unsolvability.
Louis O. Kattsoff,Martin Davis +1 more
TL;DR: Only for you today!
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Book
A Course of Modern Analysis
TL;DR: The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.
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Hilbert's tenth problem
TL;DR: This book presents the full, self-contained negative solution of Hilbert's 10th problem, and describes the many improvements and modifications of the original proof - since the problem was "unsolved" 20 years ago, and adds several new, previously unpublished proofs.
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Some undecidable problems involving elementary functions of a real variable
TL;DR: Let E be a set of expressions representing real, single valued, partially defined functions of one real variable and E * be the set of functions represented by expressions in E .
Journal ArticleDOI
The wave equation with computable initial data such that its unique solution is not computable
TL;DR: In this paper, it was shown that all non-computable solutions of the wave equation are of the type commonly referred to as weak solutions, i.e., although continuous, they are not twice differentiable at all points.