10-26 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 $ -\Delta-V(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 $H_-=-\Delta-V$.

Files: 10-26.src( 10-26.keywords , a2010.pdf.mm )