Geodesic
The divergence of spectral decompositions connected with homogeneous elliptic operators
Matematičeskie zametki, Tome 18 (1975) no. 6, pp. 887-894.

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In this work an asymptotic formula is obtained for the means of the Riesz spectral function of a homogeneous elliptic operator of arbitrary order $m\ge2$ with constant coefficients. Conditions are obtained under which localization (and convergence) of the means of the Riesz spectral decompositions of functions from the Hölder class is absent. 
@article{MZM_1975_18_6_a10,
     author = {A. K. Pulatov},
     title = {The divergence of spectral decompositions connected with homogeneous elliptic operators},
     journal = {Matemati\v{c}eskie zametki},
     pages = {887--894},
     publisher = {mathdoc},
     volume = {18},
     number = {6},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_6_a10/}
}
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A. K. Pulatov. The divergence of spectral decompositions connected with homogeneous elliptic operators. Matematičeskie zametki, Tome 18 (1975) no. 6, pp. 887-894. http://geodesic.mathdoc.fr/item/MZM_1975_18_6_a10/