$L^{p}$-computability in recursive analysis
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- by Marian Boykan Pour-El and Ian Richards PDF
- Proc. Amer. Math. Soc. 92 (1984), 93-97 Request permission
Abstract:
${L^p}$-computability is defined in terms of effective approximation; e.g. a function $f \in {L^p}[0,1]$ is called ${L^P}$-computable if $f$ is the effective limit in ${L^p}$-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 $f$ is ${L^p}$-computable if and only if (a) the sequence of Fourier coefficients of $f$ is computable, and (b) the ${L^p}$-norm of $f$ is a computable real. We show that this fails for $p = 1$.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 92 (1984), 93-97
- MSC: Primary 03F60; Secondary 03D80, 46E99, 46R05
- DOI: https://doi.org/10.1090/S0002-9939-1984-0749899-0
- MathSciNet review: 749899