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Fundamentalnaya i Prikladnaya Matematika, 1995, Volume 1, Issue 4, Pages 1125–1128
(Mi fpm123)
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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 $m>\frac{N}{2}$.
Received: 01.02.1995
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
Linking options:
https://www.mathnet.ru/eng/fpm123 https://www.mathnet.ru/eng/fpm/v1/i4/p1125
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