On Fourier multipliers and absolute convergence of Fourier integrals of radial functions - Trigub, R. M. (Ukrains’kyi Matematychnyi Zhurnal, 2010)
We obtain sufficient conditions for the representability of a function in the form of an absolutely convergent Fourier integral. These conditions are given in terms of the joint behavior of the function and its derivatives at infinity, and their efficiency and exactness are verified with the use of a known example. We also consider radial functions of an arbitrary number of variables.