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1
Content available remote

On extended eigenvalues and extended eigenvectors of truncated shift

100%
Alkanjo H.
Concrete Operators
|
2013
|
tom 1
19-27
EN
In this paper we consider the truncated shift operator Su on the model space K2u := H2 θ uH2. We say that a complex number λ is an extended eigenvalue of Su if there exists a nonzero operator X, called extended eigenvector associated to λ, and satisfying the equation SuX = λXSu. We give a complete description of the set of extended eigenvectors of Su, in the case of u is a Blaschke product..
2
Content available remote

On definitions of the pluricomplex Green function

100%
Edigarian A.
Annales Polonici Mathematici
|
1997
|
tom 67
|
nr 3
233-246
EN
We give several definitions of the pluricomplex Green function and show their equivalence.
3
Content available remote

Approximation numbers of composition operators on Hp

88%
Li D., Queffélec H., Rodríguez-Piazza L.
Concrete Operators
|
2015
|
tom 2
|
nr 1
EN
give estimates for the approximation numbers of composition operators on the Hp spaces, 1 ≤ p < ∞
4
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Convexity of sublevel sets of plurisubharmonic extremal functions

75%
Lárusson F., Lassere P., Sigurdsson R.
Annales Polonici Mathematici
|
1998
|
tom 68
|
nr 3
267-273
EN
Let X be a convex domain in ℂⁿ and let E be a convex subset of X. The relative extremal function $u_{E,X}$ for E in X is the supremum of the class of plurisubharmonic functions v ≤ 0 on X with v ≤ -1 on E. We show that if E is either open or compact, then the sublevel sets of $u_{E,X}$ are convex. The proof uses the theory of envelopes of disc functionals and a new result on Blaschke products.
5
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Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces

75%
Gu C., Luo S., Xiao J.
Complex Manifolds
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2017
|
tom 4
|
nr 1
84-119
EN
This paper gives a full characterization of the reducing subspaces for the multiplication operator Mϕ on the Dirichlet space with symbol of finite Blaschke product ϕ of order 5I 6I 7. The reducing subspaces of Mϕ on the Dirichlet space and Bergman space are related. Our strategy is to use local inverses and Riemann surfaces to study the reducing subspaces of Mϕ on the Bergman space. By this means, we determine the reducing subspaces of Mϕ on the Dirichlet space and answer some questions of Douglas-Putinar-Wang in [6].
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