Geodesic
Double trigonometric series with lacunary constant sign coefficients
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2012), pp. 33-35

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The article presents an analogue of Sidon's theorem for series of the form $$ \sum \limits_{k = 1}^\infty\sum\limits_{n=0}^\infty a_{k,n} \cos {m_k x}\cos{ny}, $$ where the coefficients $a_{k,n}$ have a constant sign for any fixed $k$. 
@article{VMUMM_2012_6_a5,
     author = {A. Zh. Ydyrys},
     title = {Double trigonometric series with lacunary constant sign coefficients},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {33--35},
     publisher = {mathdoc},
     number = {6},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2012_6_a5/}
}
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AU  - A. Zh. Ydyrys
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%T Double trigonometric series with lacunary constant sign coefficients
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%D 2012
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%I mathdoc
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%F VMUMM_2012_6_a5
A. Zh. Ydyrys. Double trigonometric series with lacunary constant sign coefficients. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2012), pp. 33-35. http://geodesic.mathdoc.fr/item/VMUMM_2012_6_a5/