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 Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find

 Fundam. Prikl. Mat., 1995, Volume 1, Issue 4, Pages 1125–1128 (Mi fpm123)

Short communications

On the convergence in $H^{s}$-norm of the spectral expansions corresponding to the differential operators with singularity

V. S. Serov

M. V. Lomonosov Moscow State University

Abstract: 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 $m>\frac{N}{2}$.

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Bibliographic databases:
UDC: 517.95

Citation: V. S. Serov, “On the convergence in $H^{s}$-norm of the spectral expansions corresponding to the differential operators with singularity”, Fundam. Prikl. Mat., 1:4 (1995), 1125–1128

Citation in format AMSBIB
\Bibitem{Ser95} \by V.~S.~Serov \paper On the convergence in $H^{s}$-norm of the spectral expansions corresponding to the differential operators with singularity \jour Fundam. Prikl. Mat. \yr 1995 \vol 1 \issue 4 \pages 1125--1128 \mathnet{http://mi.mathnet.ru/fpm123} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1791799} \zmath{https://zbmath.org/?q=an:0867.35067}