In this paper, for an arbitrary fixed compact set K, we find necessary and sufficient conditions on the Taylor expansion coefficients of entire functions of exponential type so that these functions are the Fourier image of distributions supported in K. In other words, we state the Paley–Wiener theorem in the language of Taylor expansion coefficients.

中文翻译：

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新佩利-维纳定理

在本文中，对于任意固定的紧集K，我们找到了指数型整个函数的泰勒展开系数的充要条件，从而使这些函数成为K中支持的分布的傅立叶图像。换句话说，我们用泰勒展开系数的语言陈述了Paley-Wiener定理。