sobolev disk algebra
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Reducibility for a Class of Analytic Multipliers on Sobolev Disk Algebra

2021 ◽  
Vol 41 (2) ◽  
pp. 361-370
Author(s):  
Yong Chen ◽  
Ya Liu ◽  
Chuntao Qin
Keyword(s):  
Disk Algebra ◽  
Sobolev Disk Algebra

scholarly journals A Similarity Invariant and the Commutant of some Multiplication Operators on the Sobolev Disk Algebra

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Ruifang Zhao
Keyword(s):  
Sobolev Space ◽  
Unit Disk ◽  
Analytic Functions ◽  
Entire Functions ◽  
Rational Functions ◽  
Multiplication Operators ◽  
Disk Algebra ◽  
Strongly Irreducible ◽  
Similarity Invariant ◽  
Sobolev Disk Algebra

LetR(𝔻)be the algebra generated in Sobolev spaceW22(𝔻)by the rational functions with poles outside the unit disk𝔻¯. In this paper, we study the similarity invariant of the multiplication operatorsMginℒ(R(𝔻)), whengis univalent analytic on𝔻orMgis strongly irreducible. And the commutants of multiplication operators whose symbols are composite functions, univalent analytic functions, or entire functions are studied.

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