Functional models of non-selfadjoint operators, strongly continuous semigroups, and matrix Muckenhoupt weights

One-dimensional perturbations of unbounded selfadjoint operators with empty spectrum

“…Finite rank perturbations of Volterra operators and their models in de Branges spaces also have been studied in several works by Gubreev and coathors. These papers concern Riesz bases, completeness, generation of C 0 semigroups and the relation with the so-called quasi-exponentials, see [15,14,28] and references therein. The paper by Khromov [20] treats spectral properties of finite rank perturbations of Volterra operators from a different point of view; in particular, it contains results stated in terms of the asymptotics of the kernel M(x, t) of an integral Volterra operator near the diagonal.…”