L p ‐Computability | Zendy

Zhong Ning | Zendy; Zhang BingYu | Zendy

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L p ‐Computability

Author(s) -

Zhong Ning,

Zhang BingYu

Publication year - 1999

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.19990450403

Subject(s) - computability , computable function , mathematics , function (biology) , combinatorics , discrete mathematics , computable analysis , evolutionary biology , biology

In this paper we investigate conditions for L p ‐computability which are in accordance with the classical Grzegorczyk notion of computability for a continuous function. For a given computable real number p ≥ 1 and a compact computable rectangle I ⊂ ℝ q , we show that an L p function f ∈ L p ( I ) is L P ‐computable if and only if (i) f is sequentially computable as a linear functional and (ii) the L p ‐modulus function of f is effectively continuous at the origin of ℝ q .

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