Type‐2 computability on spaces of integrable functions
Copyright policy )Type‐2 computability on spaces of integrable functions
AbstractUsing 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)
- University of Hagen Germany
Complexity of computation (including implicit computational complexity), complexity bounds, Type-2 theory of effectivity, Higher-type and set recursion theory, Fourier transform, convolution, integrable functions, Theory of numerations, effectively presented structures, computable operators, Constructive and recursive analysis
Complexity of computation (including implicit computational complexity), complexity bounds, Type-2 theory of effectivity, Higher-type and set recursion theory, Fourier transform, convolution, integrable functions, Theory of numerations, effectively presented structures, computable operators, Constructive and recursive analysis
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