On unconditional basisness of B-quasi-exponentials
Arkadi Minkin · arXiv (Cornell University) · 2010
We consider a quasinilpotent operator whose resolvent is entire operator function of exponential type. Let A be its one-dimensional perturbation. We establish necessity of Muckenhoupt condition (A2) for two weights related to operator A for unconditional basisness of its eigenfunctions. Note that no apriori restrictions are imposed on the spectrum of A.