Book Review: Tables of integral transforms

Henstock-Kurzweil Integral Transforms

Copyright q 2012 Salvador Sánchez-Perales et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We show conditions for the existence, continuity, and differentiability of functions defined by ΓΓs ∞ −∞ ftgt, sdt, where f is a func...

Global Behavior of Integral Transforms

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...

Book Review

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Basefield transforms derived from character tables

We show that it is possible to de ne Hartley-like transforms for (generalized) character tables of nite groups. This large class of transforms include Hartley transforms for discrete Fourier transforms over abelian groups and Hartley-like transforms for the discrete cosine transform of type I.

Book Review