✦ LIBER ✦

Lp-Computability

✍ Scribed by Ning Zhong; Bing-Yu Zhang

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 434 KB
Volume: 45
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.19990450403

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper we investigate conditions for LP-computability which are in ac- cordance with the classical Grzegorczyk notion of computability for a continuous function. For a given computable real number p 2 1 and a compact computable rectangle I c Rq, we show that an Lp function f E L p ( I ) is LP-computable if and only if (i) f is sequentially computable as a linear functional and (ii) the LP-modulus function of f is effectively continuous at the origin of Rq.

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