On the convergence in $H^{s}$-norm of the spectral expansions corresponding to the differential operators with singularity
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1125-1128
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 $m>\frac{N}{2}$.
@article{FPM_1995_1_4_a24,
author = {V. S. Serov},
title = {On the convergence in $H^{s}$-norm of the spectral expansions corresponding to the differential operators with singularity},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {1125--1128},
year = {1995},
volume = {1},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a24/}
}
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V. S. Serov. On the convergence in $H^{s}$-norm of the spectral expansions corresponding to the differential operators with singularity. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1125-1128. http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a24/
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