beurling theorem
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2021 ◽  
Vol 496 (2) ◽  
pp. 124765
Author(s):  
Robert T.W. Martin ◽  
Eli Shamovich
Keyword(s):  

2020 ◽  
Vol 107 (1-2) ◽  
pp. 42-53
Author(s):  
M. Elloumi ◽  
A. Baklouti ◽  
S. Azaouzi
Keyword(s):  

2018 ◽  
Vol 70 (3) ◽  
pp. 515-537 ◽  
Author(s):  
Yanni Chen ◽  
Don Hadwin ◽  
Zhe Liu ◽  
Eric Nordgren

AbstractThe object of this paper is to prove a version of the Beurling–Helson–Lowdenslager invariant subspace theorem for operators on certain Banach spaces of functions on a multiply connected domain in ℂ. The norms for these spaces are either the usual Lebesgue and Hardy space norms or certain continuous gauge norms. In the Hardy space case the expected corollaries include the characterization of the cyclic vectors as the outer functions in this context, a demonstration that the set of analytic multiplication operators is maximal abelian and reflexive, and a determination of the closed operators that commute with all analytic multiplication operators.


2016 ◽  
Vol 86 (3) ◽  
pp. 321-332
Author(s):  
Yanni Chen ◽  
Don Hadwin ◽  
Ye Zhang

2016 ◽  
Vol 75 (2) ◽  
pp. 497-523 ◽  
Author(s):  
Yanni Chen ◽  
Don Hadwin ◽  
Junhao Shen

1966 ◽  
Vol 18 ◽  
pp. 240-255 ◽  
Author(s):  
Morisuke Hasumi

The purpose of this paper is to extend various invariant subspace theorems for the circle group to multiply connected domains. Such attempts are not new. Actually, Sarason (4) studied the invariant subspaces of annulus operators acting on L2 and showed certain parallelisms between the unit disk case and the annulus case. Voichick (8) observed analytic functions on a finite Riemann surface and generalized the Beurling theorem on the closed invariant subspaces of H2 as well as the Beurling–Rudin theorem on the closed ideals of the disk algebra. Here we shall consider LP(Γ) and C(Γ) defined on the boundary Γ of a finite orientable Riemann surface R.


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