 1026 Oleg Safronov
 Lower bounds on the eigenvalue sums of the Schr\"odinger operator and the spectral conservation law
(280K, pdf)
Jan 28, 10

Abstract ,
Paper (src),
View paper
(auto. generated pdf),
Index
of related papers

Abstract. In the first part of the paper we consider the Schr\"odinger operator
$
\DeltaV(x),\quad V>0.
$
We discuss the relation between the behavior of $V$ at the infinity and the properties of the negative spectrum of $H$.
After that, we consider the case when $V$ changes its sign:
$
V=V_+V_,\qquad 2V_\pm=V\pm V.
$
In this case, we treat $V$ and $V$ symmetrically and study the relation between the behavior of $V$ at the infinity and the negative spectra of the operators $H_+=\Delta+V$ and $H_=\DeltaV$.
 Files:
1026.src(
1026.keywords ,
a2010.pdf.mm )