Geodesic
On the representation of a~function as an absolutely convergent Fourier integral
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and differential equations, Tome 269 (2010), pp. 153-166.

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We obtain new sufficient conditions for the representability of a function by an absolutely convergent Fourier integral in $\mathbb R^d$. These conditions are given in terms of the simultaneous behavior of a function and its derivatives at $\infty$. We test the sharpness of the conditions using well-known examples. 
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E. R. Liflyand; R. M. Trigub. On the representation of a~function as an absolutely convergent Fourier integral. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and differential equations, Tome 269 (2010), pp. 153-166. http://geodesic.mathdoc.fr/item/TM_2010_269_a12/

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