Geodesic
On Fourier transformation of a class of entire functions
Ufa mathematical journal, Tome 6 (2014) no. 4, pp. 108-121 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a space of entire functions of several complex variables decaying fast on $\mathbb R^n$ and such that their growth along $i\mathbb R^n$ is majorized by means of a family of weight functions. Under certain assumptions for the weight functions we obtain an equivalent description of this space in terms of estimates for partial derivatives of the functions in $\mathbb R^n$ and prove a Paley–Wiener type theorem.
Keywords: Gelfand–Shilov spaces, entire functions, convex functions.
Mots-clés : Fourier transform 
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I. Kh. Musin; M. I. Musin. On Fourier transformation of a class of entire functions. Ufa mathematical journal, Tome 6 (2014) no. 4, pp. 108-121. http://geodesic.mathdoc.fr/item/UFA_2014_6_4_a8/

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