Geodesic
Spaces of generalised smoothness in summability problems for $\Phi$-means of spectral decomposition
Eurasian mathematical journal, Tome 5 (2014) no. 1, pp. 61-81

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We establish conditions for localization of generalised Riesz means of spectral decomposition by system of fundamental functions of Laplace operator in terms of belongingness of the decomposing function to the spaces of generalised smoothness. 
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     title = {Spaces of generalised smoothness in summability problems for $\Phi$-means of spectral decomposition},
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T. G. Ayele; M. L. Goldman. Spaces of generalised smoothness in summability problems for $\Phi$-means of spectral decomposition. Eurasian mathematical journal, Tome 5 (2014) no. 1, pp. 61-81. http://geodesic.mathdoc.fr/item/EMJ_2014_5_1_a1/