The discrete spectrum in the singular Friedrichs model

dc.creatorYafaev, D.
dc.date1998-06-15
dc.date.accessioned2026-07-07T04:32:26Z
dc.date.available2026-07-07T04:32:26Z
dc.descriptionA typical result of the paper is the following. Let $H_γ=H_0 +γV$ 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 $H_γ$ has infinite number of negative eigenvalues for any coupling constant $γ\neq 0$. For other values of $l$, the negative spectrum of $H_γ$ is infinite for $|γ|> σ_l$ where $σ_l$ is some explicit positive constant. In the case $\pm γ\in (0,σ_l]$, the number $N^{(\pm)}_l$ of negative eigenvalues of $H_γ$ is finite and does not depend on $γ$. We calculate $N^{(\pm)}_l$.
dc.descriptionLatex
dc.identifierhttps://arxiv.org/abs/math-ph/9806009
dc.identifierhttp://arxiv.org/abs/math-ph/9806009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58187
dc.subjectMathematical Physics
dc.subject35J10; 47A75; 81U20
dc.titleThe discrete spectrum in the singular Friedrichs model
dc.typetext

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