Description of extended eigenvalues and extended eigenvectors of integration operators on the Wiener algebra
نویسنده
چکیده
In the present paper we consider the Volterra integration operator V on the Wiener algebra W (D) of analytic functions on the unit discD of the complex plane C. A complex number is called an extended eigenvalue of V if there exists a nonzero operator A satisfying the equation AV = V A. We prove that the set of all extended eigenvalues of V is precisely the set C\{0}, and describe in terms of Duhamel operators and composition operators the set of corresponding extended eigenvectors of V . The similar result for some weighted shift operator on p spaces is also obtained. 2008 Elsevier GmbH. All rights reserved. MSC 2000: primary 47A15; 47A65; secondary 47B38
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