• Corpus ID: 119152368

The discrete spectrum in the singular Friedrichs model

@inproceedings{DYafaev1998TheDS,
  title={The discrete spectrum in the singular Friedrichs model},
  author={D.Yafaev},
  year={1998}
}

• D.Yafaev
• Published 15 June 1998
• Mathematics

A typical result of the paper is the following. Let $H_\gamma=H_0 +\gamma V$ where $H_0$ is multiplication by $|x|^{2l}$ and $V$ is an integral operator with kernel $\cos<x,y\rang le$ in the space $L_2(R^d)$. If $l=d/2+ 2k$ for some $k= 0,1,...$, then the operator $H_\gamma$ has infinite number of negative eigenvalues for any coupling constant $\gamma\neq 0$. For other values of $l$, the negative spectrum of $H_\gamma$ is infinite for $|\gamma|>\sigma_l$ where $\sigma_l$ is some explicit positive constant. In the case $\pm \gamma\in (0,\sigma_l]$, the number $N^{(\pm)}_l$ of negative eigenvalues of $H_\gamma$ is finite and does not depend on $\gamma$. We calculate $N^{(\pm)}_l$.