摘要
In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequence of L^(1)functions converging to the given function and verifying their representation in the form of Fourier transform to establish the desired result of the given function.Applying this main result,we further generalize the Paley-Wiener theorem for band-limited functions to the analytic function spaces L^(p)(0<p<∞)with general weights.
本文将Paley-Wiener定理推广至带一般权的解析函数空间中.首先,通过构造一个收敛于目标函数的L^(1)函数列,验证函数列中函数具有Fourier变换表示,进而得到管状区域上带一般权的Hardy空间Hp(0<p<∞)函数的积分表示结论.接着,应用这一主要结论,将带限函数的Paley-Wiener定理推广到带一般权的解析函数空间L^(p)(0<p<∞)中.
出处
《应用数学》
北大核心
2025年第3期841-849,共9页
Mathematica Applicata
基金
Supported by the National Natural Science Foundation of China(12301101)
the Guangdong Basic and Applied Basic Research Foundation(2022A1515110019 and 2020A1515110585)。
