161433
20181203022233.0
ARTICLE
Undecidable propositions by ODE's
2007
2007
Journal Articles
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.
Buser, Peter
104683
244696
Scarpellini, Bruno
317-340
2
Annales Academiae Scientiarum Fennicae, Mathematica
32
GEOM
252345
U10122
oai:infoscience.tind.io:161433
article
SB
139598
EPFL-ARTICLE-161433
1117.03068/GEOM
EPFL
PUBLISHED
REVIEWED
ARTICLE