Geodesic
Absolute convergence of Fourier series in eigenfunctions of an elliptic operator
Matematičeskie zametki, Tome 19 (1976) no. 3, pp. 435-448.

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In this article we investigate absolute convergence of Fourier series in eigenfunctions of an $m$-th order elliptic operator on functions in the Besov class $B_{2,\theta}^{N/2}$. We show that in terms of Besov classes the theorem of Peetre on absolute convergence of series in eigenfunctions in the class $B_{2,1}^{N/2}$ is best possible. We construct a function in $B_{2,\theta}^{N/2}$ whose Fourier series is absolutely divergent at any preassigned point. 
@article{MZM_1976_19_3_a12,
     author = {V. S. Serov},
     title = {Absolute convergence of {Fourier} series in eigenfunctions of an elliptic operator},
     journal = {Matemati\v{c}eskie zametki},
     pages = {435--448},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_3_a12/}
}
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V. S. Serov. Absolute convergence of Fourier series in eigenfunctions of an elliptic operator. Matematičeskie zametki, Tome 19 (1976) no. 3, pp. 435-448. http://geodesic.mathdoc.fr/item/MZM_1976_19_3_a12/