On unconditional basisness of B-quasi-exponentials

Abstract

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.

arXiv commentAmsLatex, 13 pages. Changed formualtion of Lemma 3.3 and reworked Lemma 3.1