On the extended eigenvalues and extended eigenvectors of shift operator on the Wiener algebra
APPLIED MATHEMATICS LETTERS, cilt.22, sa.11, ss.1727-1729, 2009 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 22 Sayı: 11
- Basım Tarihi: 2009
- Doi Numarası: 10.1016/j.aml.2009.06.008
- Dergi Adı: APPLIED MATHEMATICS LETTERS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1727-1729
- Anahtar Kelimeler: Wiener algebra, Extended eigenvalue, Extended eigenvector, Shift operator
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
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 lambda is called an extended eigenvalue of S if there exists a nonzero operator A satisfying the equation AS = lambda SA. We prove that the set of all extended eigenvalues of S is precisely the set (D) over bar, and describe in terms of multiplication operators and composition operators the set of all corresponding extended eigenvectors of S. (C) 2009 Elsevier Ltd. All rights reserved.