000161433 001__ 161433
000161433 005__ 20180925134120.0
000161433 037__ $$aARTICLE
000161433 245__ $$aUndecidable propositions by ODE's
000161433 269__ $$a2007
000161433 260__ $$c2007
000161433 336__ $$aJournal Articles
000161433 520__ $$aThe 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.
000161433 700__ $$0244696$$aBuser, Peter$$g104683
000161433 700__ $$aScarpellini, Bruno
000161433 773__ $$j32$$k2$$q317-340$$tAnnales Academiae Scientiarum Fennicae, Mathematica
000161433 909C0 $$0252345$$pGEOM$$xU10122
000161433 909CO $$ooai:infoscience.tind.io:161433$$pSB$$particle
000161433 917Z8 $$x139598
000161433 937__ $$aEPFL-ARTICLE-161433
000161433 970__ $$a1117.03068/GEOM
000161433 973__ $$aEPFL$$rREVIEWED$$sPUBLISHED
000161433 980__ $$aARTICLE