Type‐2 computability on spaces of integrable functions

Mathematical Logic Quarterly 50 (4):417-430 (2004)
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Abstract

Using Type‐2 theory of effectivity, we define computability notions on the spaces of Lebesgue‐integrable functions on the real line that are based on two natural approaches to integrability from measure theory. We show that Fourier transform and convolution on these spaces are computable operators with respect to these representations. By means of the orthonormal basis of Hermite functions in L2, we show the existence of a linear complexity bound for the Fourier transform. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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10.1002/malq.200310109

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Computational complexity on computable metric spaces.Klaus Weirauch - 2003 - Mathematical Logic Quarterly 49 (1):3-21.
Lp -Computability.Ning Zhong & Bing-Yu Zhang - 1999 - Mathematical Logic Quarterly 45 (4):449-456.

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