Analysis Seminar: "Finite rank $d$ perturbations"
Abstract: Kato-Rosenblum theorem and Aronszajn-Donoghue theory provide us with reasonably good understanding of the subtle theory of rank one $d=1$ perturbations. We will briefly discuss these statements. When $d>1$, the situation is different. While the Kato-Rosenblum theorem still ensures the stability of the absolutely continuous part of the spectrum, the singular parts’ behavior may be more complex. Nonetheless, some positive results prevail in the finite rank setting.
Host: Brett Wick