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A space of slowly decreasing functions with pleasant Fourier transforms
Published online by Cambridge University Press: 14 November 2011
Synopsis
The space in question is Aµ(R):=L1(R) + Bµ(R), where Bµ(R) is a Banach space that contains the “tails” (the dominant parts for large values of |x|) of certain slowly decreasing functions from R to R. Functions in Bµ(R) are of bounded variation, and the norm involves their variation and a weighting function. Theorems are proved only for Bµ(R), because those for L1(R) are known. The results concern the convolution of a function in Bµ(R) with one in L1(R), the Fourier transform acting on Bµ(R), and the signum rule for the Hilbert transform of functions in Bµ(R).
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 119 , Issue 1-2 , 1991 , pp. 73 - 86
- Copyright
- Copyright © Royal Society of Edinburgh 1991
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