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On definitions of the pluricomplex Green function

100%

Edigarian A.

Annales Polonici Mathematici

1997

tom 67

nr 3

233-246

We give several definitions of the pluricomplex Green function and show their equivalence.

On extended eigenvalues and extended eigenvectors of truncated shift

100%

Alkanjo H.

Concrete Operators

2013

tom 1

19-27

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..

Blaschke products, (alpha)-curves and Qp spaces

100%

Majchrowska G. , Mouratides C.

Demonstratio Mathematica

2010

tom Vol. 43, nr 1

29-38

We give necessary and sufficient conditions for Blaschke products with zeros on an a-curve, to belong to a Qp space, in terms only of distribution of the zeros. It comes out that the condition depends on p. As we see the 0-1 law of the non tangential case breaks. Here it is possible that a Blaschke product B belongs to Qp for some but not for all p.

Approximation numbers of composition operators on Hp

88%

Li D. , Queffélec H. , Rodríguez-Piazza L.

Concrete Operators

2015

tom 2

nr 1

give estimates for the approximation numbers of composition operators on the Hp spaces, 1 ≤ p < ∞

Geometric result in the boundary behaviour of Blaschke products

88%

Mouratidis C.

Journal of Mathematics and Applications

2009

tom Vol. 31

91-97

For a Blaschke product B with zeros in an angular domain having vertex on the unit circle we give a necessary and sufficient condition for the boundary behavior of B, in terms only of the distribution of the zeros. Moreover, we show, with a counterexample, the non-equivalence of two known results of Tanaka, concerning the specific boundary behavior of Blaschke products.

Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces

75%

Gu C. , Luo S. , Xiao J.

Complex Manifolds

2017

tom 4

nr 1

84-119

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].

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

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.