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

被引：13
|
作者：
Gurdal, M. [1 ]
机构：
[1] Suleyman Demirel Univ, Dept Math, TR-32260 Isparta, Turkey
来源：
APPLIED MATHEMATICS LETTERS | 2009年 / 22卷 / 11期
关键词：
Wiener algebra; Extended eigenvalue; Extended eigenvector; Shift operator;
D O I：
10.1016/j.aml.2009.06.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：1727 / 1729
页数：3
相关论文
共 50 条
  • [1] Description of extended eigenvalues and extended eigenvectors of integration operators on the Wiener algebra
    Gurdal, M.
    [J]. EXPOSITIONES MATHEMATICAE, 2009, 27 (02) : 153 - 160
  • [2] On extended eigenvalues and extended eigenvectors of truncated shift
    Alkanjo, Hasan
    [J]. CONCRETE OPERATORS, 2013, 1 : 19 - 27
  • [3] On extended eigenvalues and extended eigenvectors of some operator classes
    Karaev, MT
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 134 (08) : 2383 - 2392
  • [4] Extended eigenvalues and the volterra operator
    Biswas, A
    Lambert, A
    Petrovic, S
    [J]. GLASGOW MATHEMATICAL JOURNAL, 2002, 44 : 521 - 534
  • [5] Extended Eigenvalues of a Closed Linear Operator
    Ammar, Aymen
    Boutaf, Fatima Zohra
    Jeribi, Aref
    [J]. FILOMAT, 2022, 36 (13) : 4277 - 4291
  • [6] Weighted shift operators and extended eigenvalues
    Hussein, Kareem M.
    Ahmed, Buthainah A.
    [J]. JOURNAL OF INTERDISCIPLINARY MATHEMATICS, 2023, 26 (05) : 849 - 855
  • [7] The set of extended eigenvalues of a weighted Toeplitz operator
    Lauric, Vasile
    [J]. ACTA SCIENTIARUM MATHEMATICARUM, 2006, 72 (3-4): : 691 - 700
  • [8] Extended operator algebra for Abelian sandpile models
    Dhar, D
    [J]. PHYSICA A, 1996, 224 (1-2): : 162 - 168
  • [9] Extended operator algebra and reducibility in the WZW permutation orbifolds
    Halpern, MB
    Helfgott, C
    [J]. INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 2003, 18 (10): : 1773 - 1826
  • [10] Extended eigenvalues of 2 x 2 block operator matrices
    Ammar, Aymen
    Boutaf, Fatima Zohra
    Jeribi, Aref
    [J]. FILOMAT, 2023, 37 (05) : 1377 - 1389
12345