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Type-2 computability on spaces of integrable functions

✍ Scribed by Daren Kunkle

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
238 KB
Volume
50
Category
Article
ISSN
0044-3050

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✦ Synopsis

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 L~2~, 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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