T. G. Ayele, M. L. Goldman, “Spaces of generalised smoothness in summability problems for <nobr>$\Phi$</nobr>-means of spectral decomposition”, Eurasian Math. J., 2014, Volume 5, Number 1,Pages <nobr>61

Spaces of generalised smoothness in summability problems for $\Phi$-means of spectral decomposition

T. G. Ayele^a, M. L. Goldman^b

^a Department of Mathematics, Addis Ababa University, Addis Ababa, Ethiopia
^b Department of nonlinear analysis and optimization, Peoples' Friendship University of Russia, 6 Miklukho–Maklaya, 117198 Moscow, Russia

Abstract: 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.

Keywords and phrases: spectral decompositions, summation method, principle of localization, spaces of generalised smoothness.

MSC: 46E35, 54C35, 35B65

Received: 27.05.2012

Language: English