TY - EJOUR
AB - 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.
T1 - Undecidable propositions by ODE's
IS - 2
DA - 2007
AU - Buser, Peter
AU - Scarpellini, Bruno
JF - Annales Academiae Scientiarum Fennicae, Mathematica
SP - 317-340
VL - 32
EP - 317-340
ID - 161433
ER -