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research article
Undecidable propositions by ODE's
The authors define a family of functions by starting with (complex) exponentials and closing under some basic algebraic operations, integration, and solution of certain systems of differential equations. They then show that for every recursively (computably) enumerable set $S$ -- in particular, even when $S$ is not computable -- there exists a function $f$ in the family whose Fourier coefficients int_-pi^pif(x),e^-inxdx are nonzero for precisely those $n$ in $S$. The paper concludes with some speculative remarks regarding hypercomputation.
Type
research article
Authors
Publication date
2007
Volume
32
Issue
2
Start page
317
End page
340
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
December 3, 2010
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