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 $m > \frac N2$.
All articles are
published in Russian.
Location: http://mech.math.msu.su/~fpm/eng/95/954/95425.htm
Last modified: October 15, 1997.