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. 
@article{TM_2010_269_a12,
     author = {E. R. Liflyand and R. M. Trigub},
     title = {On the representation of a~function as an absolutely convergent {Fourier} integral},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {153--166},
     publisher = {mathdoc},
     volume = {269},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_269_a12/}
}
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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/