The paper contains two main results. First we describe one-dimensional Franklin series converging everywhere except possibly on a finite set to an everywhere-finite integrable function. Second we establish a class of subsets of ##IMG## [http://ej.iop.org/images/1064-5632/84/5/829/IZV_84_5_829ieqn1.gif] {$[0, 1]^2$} with the following property. If a double Franklin series converges everywhere except on this set to an everywhere-finite integrable function, then it is the Fourier–Franklin series of this function. In particular, all countable sets are in this class.

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一维和双重富兰克林级数的唯一性定理

本文包含两个主要结果。首先，我们描述一维富兰克林级数，该级数可以在各处收敛，除了可能在到处都是有限可积函数的有限集上。其次，我们建立## IMG ##的子集类别[http://ej.iop.org/images/1064-5632/84/5/829/IZV_84_5_829ieqn1.gif] {$ [0，1] ^ 2 $ }，并具有以下属性。如果一个双富兰克林级数收敛到该集合以外的任何地方，到一个无处不在有限的可积函数，那么它就是该函数的傅里叶-富兰克林级数。特别是，所有可数集都在此类中。