Mathematics – Spectral Theory
Scientific paper
2010-01-22
Mathematics
Spectral Theory
AmsLatex, 13 pages. Changed formualtion of Lemma 3.3 and reworked Lemma 3.1
Scientific paper
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.
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