Uniqueness problem and growth property for Fourier transform of functions in the upper half-space. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Xu, Zuoliang; Zhang, Yanhui
• Is Part Of: Applicable analysis. Volume 101:Issue 1(2022)
• Page Start: 100
• Page End: 107
• Publication Date: 2022-01-02
• Subjects: Yongzhi Steve Xu; Fourier transform -- uniqueness -- C class; 31B05 -- 31B10; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1729357
• Languages: English
• ISSNs: 0003-6811

Abstract

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 C . We further prove the growth property involving of the Fourier transform of functions in L 2 in the upper half-space of R n, which partly generalizes the result in Levi [Lectures on entire functions. Providence (RI): American Mathematical Society; 1996].