Ufa Mathematical Journal
    Volume 6, Number 4, pp. 108-121

    On Fourier transform of a class of entire functions

    Musin M.I., Musin I.Kh.


    Download PDF
    Article on MathNet


    We consider a space of entire functions of several complex variables decaying fast on ${\mathds{R}}^n$ and such that their growth along $i{\mathds{R}}^n$ 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 ${\mathds{R}}^n$ and prove a Paley-Wiener type theorem.