Slowly growing subharmonic function II.
Slowly growing subharmonic functions I.
Some remarks on largest subharmonic minorants.
Some results on thin sets in a half plane
When one is restricted to a Stolz domain in a half plane we prove that internal thinness of a set at the origin structly implies minimal thinness there. Furthermore this result extends to the half plane itself. We also work out some relations among the concepts of minimal thinness, semi-thinness and finite logarithmic length. Finally we show that a theorem of Ahlfors and Heins can be improved.
Some simple proofs in holomorphic spectral theory
This paper gives some very elementary proofs of results of Aupetit, Ransford and others on the variation of the spectral radius of a holomorphic family of elements in a Banach algebra. There is also some brief discussion of a notorious unsolved problem in automatic continuity theory.
Subharmonic analogues of MacLane's classes
Subharmonicity for areal Bloch-function criteria
Subharmonicity in von Neumann algebras
Let ℳ be a von Neumann algebra with unit . Let τ be a faithful, normal, semifinite trace on ℳ. Given x ∈ ℳ, denote by the generalized s-numbers of x, defined by = inf||xe||: e is a projection in ℳ i with ≤ t (t ≥ 0). We prove that, if D is a complex domain and f:D → ℳ is a holomorphic function, then, for each t ≥ 0, is a subharmonic function on D. This generalizes earlier subharmonicity results of White and Aupetit on the singular values of matrices.
Substochastic transition operators on trees and their associated Poisson integrals
Superharmonic functions and bounded point evaluations.
Sur le problème de Dirichlet
Sur les fonctions harmoniques et holomorphes de classe et le problème de Ginzburg-Landau en deux dimensions
Sur l’espace
Sur une propriété générale des fonctions harmoniques
The Berezin transform and operators on spaces of analytic functions
In this article we will illustrate how the Berezin transform (or symbol) can be used to study classes of operators on certain spaces of analytic functions, such as the Hardy space, the Bergman space and the Fock space. The article is organized according to the following outline. 1. Spaces of analytic functions 2. Definition and properties Berezin transform 3. Berezin transform and non-compact operators 4. Commutativity of Toeplitz operators 5. Berezin transform and Hankel or Toeplitz operators 6....
The Cauchy transform of continuous linear functionals and projections on the weighted spaces of analytic functions.
The Dirichlet problem for harmonic functions with boundary values from Zygmund classes.
The Dirichlet problem for harmonic maps from the disk into the euclidean n-sphere
The Generalized Ahlfors-Heins Theorem in Certain d-Dimensional Cones.
The minimum modulus of a subharmonic function