Open Access
March 2004 Computable sequences in the Sobolev spaces
Shoki Miyamoto, Atsushi Yoshikawa
Proc. Japan Acad. Ser. A Math. Sci. 80(3): 15-17 (March 2004). DOI: 10.3792/pjaa.80.15


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 $s$, $0 \le s < 1$.


Download Citation

Shoki Miyamoto. Atsushi Yoshikawa. "Computable sequences in the Sobolev spaces." Proc. Japan Acad. Ser. A Math. Sci. 80 (3) 15 - 17, March 2004.


Published: March 2004
First available in Project Euclid: 18 May 2005

zbMATH: 1060.46058
MathSciNet: MR2046260
Digital Object Identifier: 10.3792/pjaa.80.15

Primary: 03D25
Secondary: 46A35

Keywords: Effective and non-effective convergence , Sobolev Spaces

Rights: Copyright © 2004 The Japan Academy

Vol.80 • No. 3 • March 2004
Back to Top