Infinite discrete spectrum in Fredholm-type partial integral operators with structured kernels

In this talk we study spectral properties of bounded self-adjoint partial integral operators in $L_2,$ generated by incomplete orthonormal systems and realized as non-compact perturbations of multiplication operators. Using direct integral decomposition, the spectrum is described via essential ranges, and the appearance of an additional spectral component at zero is established. For operators with degenerate kernels, we obtain sufficient conditions for the existence of infinitely many eigenvalues below the essential spectrum, corresponding to the Efimov effect.