Geodesic
A~resonance theorem and series in eigenfunctions of the Laplacian
Izvestiya. Mathematics , Tome 6 (1972) no. 4, pp. 788-806.

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By means of a resonance theorem we will establish the existence of functions in $L_p(\Omega)$ (where $\Omega$ is an $N$-dimensional region) whose expansion in eigenfunctions of the Laplacian is not Riesz-summable of order $a$ if $1\leqslant p\frac{2N}{N+1}$. 
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E. M. Nikishin. A~resonance theorem and series in eigenfunctions of the Laplacian. Izvestiya. Mathematics , Tome 6 (1972) no. 4, pp. 788-806. http://geodesic.mathdoc.fr/item/IM2_1972_6_4_a6/

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