Uniqueness Theorems for Multiple Franklin Series Converging over Rectangles

被引:0
|
作者
Gevorkyan, G. G. [1 ]
Hakobyan, L. A. [1 ]
机构
[1] Yerevan State Univ, Yerevan 375025, Armenia
关键词
Franklin system; multiple series; uniqueness theorem;
D O I
10.1134/S0001434621010247
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
It is proved that if a multiple series in the Franklin system converges in the sense of Pringsheim everywhere, except, perhaps, on a set that is a Cartesian product of sets of measure zero, to an everywhere finite integrable function, then it is the Fourier-Franklin series of this function. A uniqueness theorem is also proved for multiple Franklin series whose rectangular partial sums at each point have a sequential limit.
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页码:208 / 217
页数:10
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