Global Behavior of Integral Transforms
نویسنده
چکیده
It should be remarked that asymptotic estimates of the behavior of the sine and of other integral transforms of regularly varying functions [6] in terms of the function f (1/x) had been obtained before [7–9], both as x → 0 and as x →∞. However, (1.1) is a global estimate that not only considers the endpoint behavior but also holds for all x > 0. Our aim in this article is to generalize (1.1) in two directions. On the one hand, we want to consider other kernels than sine, so we will give conditions on the kernel k(x)
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