A space of slowly decreasing functions with pleasant Fourier transforms
1991 ◽
Vol 119
(1-2)
◽
pp. 73-86
Keyword(s):
SynopsisThe 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).
Keyword(s):
2017 ◽
Vol 15
(04)
◽
pp. 1750031
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2014 ◽
Vol 18
(1)
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pp. 19
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Keyword(s):
2020 ◽
Vol 457
◽
pp. 116432