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On the extended eigenvalues and extended eigenvectors of shift operator on the Wiener algebra

✍ Scribed by M. Gürdal

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
277 KB
Volume
22
Category
Article
ISSN
0893-9659

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✦ Synopsis

In the present paper we consider the shift operator S on the Wiener algebra W (D) of analytic functions on the unit disc D of the complex plane C. A complex number λ is called an extended eigenvalue of S if there exists a nonzero operator A satisfying the equation AS = λSA. We prove that the set of all extended eigenvalues of S is precisely the set D, and describe in terms of multiplication operators and composition operators the set of all corresponding extended eigenvectors of S.

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