Abstract
Pour-El and Richards [5] discussed computable smooth functions with non-computable first derivatives. We show that a similar result holds in the case of Sobolev spaces by giving a non-computable $\mathcal{H}^1(0,1)$-element which, however, is computable in any of larger Sobolev spaces $\mathcal{H}^s(0,1)$ for any computable $s$, $0 \le s < 1$.
Citation
Shoki Miyamoto. Atsushi Yoshikawa. "Computable sequences in the Sobolev spaces." Proc. Japan Acad. Ser. A Math. Sci. 80 (3) 15 - 17, March 2004. https://doi.org/10.3792/pjaa.80.15
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