Computable sequences in the Sobolev spaces

Computable sequences in the Sobolev spaces

Shoki Miyamoto and Atsushi Yoshikawa

Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 80, Number 3 (2004), 15-17.

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

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Primary Subjects: 03D25

Secondary Subjects: 46A35

Keywords: Effective and non-effective convergence; Sobolev spaces

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pja/1116442134
Mathematical Reviews number (MathSciNet): MR2046260
Zentralblatt MATH identifier: 1060.46058
Digital Object Identifier: doi:10.3792/pjaa.80.15

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