The divergence of spectral decompositions connected with homogeneous elliptic operators

A. K. Pulatov

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 517.4

Received: 23.10.1974

 English version: Mathematical Notes, 1975, 18:6, 1115–1118

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