The divergence of spectral decompositions connected with homogeneous elliptic operators

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.