- 期刊
A DISTRIBUTIONAL HARDY TRANSFORMATION
並列摘要
The Hardy's F-transform F(t) = ʃ_0^∞ F_ν(ty) yf (y) dy is extended to distributions. The corresponding inversion formula f(x) = ʃ_0^∞ c_ν(tx) t F(t)dt is shown to be valid in the weak distributional sense. This is accomplished by transferring the inversion formula onto the testing function space for the generalized functions under consideration and then showing that the limiting process in the resulting formula converges with respect to the topology of the testing function space.
延伸閱讀
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