FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1995, VOLUME 1, NUMBER 4, PAGES 1125-1128

On the convergence in Hs-norm of the spectral expansions corresponding to the differential operators with singularity

V.S.Serov

In this work we prove the convergence in the norm of the Sobolev spaces $H^s (\mathbb{R}^N)$ of the spectral expansions corresponding to the self-adjont extansions in $L^2 (\mathbb{R}^N)$ of the operators in the following way:

A(x,D) = P(D) + Q(x),
where P(D) is the self-adjont elliptic operator with constant coefficients and of order m and real potential Q(x) belongs to Kato space. As a consequence of this result we have the uniform convergence of these expansions for the case $m > \frac N2$.

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