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L p -Computability in Recursive Analysis

1984
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Proceedings of the American Mathematical Society
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Lp-computability is defined in terms of effective approximation; e.g. a function / G Lp[0,1] is called Lp-computable if / is the effective limit in Lp-norm of a computable sequence of polynomials. Other families of functions can replace the polynomials; see below. In this paper we investigate conditions which are not based on approximation. For p > 1, we show that / is Lp-computable if and only if (a) the sequence of Fourier coefficients of / is computable, and (b) the Lp-norm of / is a

doi:10.2307/2045162
fatcat:ckazkps7wzgiljbw3cc5bwix3q