(untitled) (Web of Scientists and Scholars: Journal of Multidisciplinary Research, 2025)
This article investigates the spectral properties of the Friedrichs model with an excitation rank equal to three. The model is analyzed within the framework of functional analysis and operator theory. The focus is on the structure of the spectrum, including the absolutely continuous spectrum, point spectrum, and possible singular continuous spectrum. Special attention is given to the role of the excitation rank in shaping the spectral behavior and the interaction between discrete and continuous spectral components. Analytical techniques are employed to derive explicit conditions for the appearance of eigenvalues embedded in the continuous spectrum.