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- W2319315237 abstract "It is known that under special conditions, Fourier sine transforms and Fourier cosine transforms behave asymptotically like a power of x, either as x → 0 or as x → ∞ or both. For example ( 3 ), where f(x) = x –α ϕ(x), 0 < α < 1, and ϕ(x) is of bounded variation in (0, ∞) and F c (x) is the Fourier cosine transform of f(x). This suggests that other results connecting the behaviour of a function at infinity with the behaviour of its Fourier or Watson transform near the origin might exist. In this paper wre derive various such results. For example, a special case of these results is where f (x) is the Fourier sine transform of g(x). It should be noted that the Fourier inversion formula fails to give f (+0) directly in this case. Some applications of these results to show the relationships between various forms of known summation formulae are given." @default.
- W2319315237 created "2016-06-24" @default.
- W2319315237 creator A5076890985 @default.
- W2319315237 date "1969-01-01" @default.
- W2319315237 modified "2023-09-25" @default.
- W2319315237 title "Some Results Relating the Behaviour of Fourier Transforms Near the Origin and at Infinity" @default.
- W2319315237 cites W1523050803 @default.
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- W2319315237 doi "https://doi.org/10.4153/cjm-1969-103-5" @default.
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