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In this article, we non-trivially prove the higher dimensional version of uniqueness theorem that established by M. M. Dzhrbashyan in the complex plane. We further prove the growth property involving of the Fourier transform of functions inin the upper half-space ofwhich partly generalizes the result in Levi [Lectures on entire functions. Providence (RI): American Mathematical Society; 1996].

Uniqueness problem and growth property for Fourier transform of functions in the upper half-space