Spectral properties of the Friedrichs model with involution

G. A. Agafonkin

Lomonosov Moscow State University

Abstract: We consider the spectral problem for the operator
$$ Af(x)=ixf(-x)+\int_{-1}^1K(x,y)f(y)\,dy $$
acting in $L_2[-1,1]$. For a certain class of kernels $K$, we prove the finiteness of the discrete spectrum of the operator $A$. In the case of a finite-dimensional perturbation, we also obtain sufficient conditions for the emptiness of the discrete spectrum.

Keywords: Friedrichs model, discrete spectrum.

UDC: 517

Received: 15.09.2024

DOI: 10.4213/mzm14510

 English version: Mathematical Notes, 2025, 117:1, 3–13

Bibliographic databases:

• 
•