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

Abstract

In this article, we non-trivially prove the higher dimensional version of uniqueness theorem that established by M. M. Dzhrbashyan in the complex plane $\mathbb{C}$. We further prove the growth property involving of the Fourier transform of functions in $L^2$ in the upper half-space of ${\mathbb{R}}^n,$ which partly generalizes the result in Levi [Lectures on entire functions. Providence (RI): American Mathematical Society; 1996].

COMMUNICATED BY:

• Yongzhi Steve Xu

Keywords:

• Fourier transform
• uniqueness
• C class

MR(2000) Subject Classifications:

• 31B05
• 31B10

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was partly supported by National Natural Science Foundation of China [grant numbers 11971042, 11571365] and Natural Science Foundation of Beijing Municipality [grant number 1182008].