Singularity of parabolic measures
Slowly growing subharmonic function II.
Slowly growing subharmonic functions I.
Small values of polynomials: Cartan, Pólya and others.
Smoothness of Green's functions and Markov-type inequalities
Let E be a compact set in the complex plane, be the Green function of the unbounded component of with pole at infinity and where the supremum is taken over all polynomials of degree at most n, and . The paper deals with recent results concerning a connection between the smoothness of (existence, continuity, Hölder or Lipschitz continuity) and the growth of the sequence . Some additional conditions are given for special classes of sets.
Smoothness of the Green function for a special domain
We consider a compact set K ⊂ ℝ in the form of the union of a sequence of segments. By means of nearly Chebyshev polynomials for K, the modulus of continuity of the Green functions is estimated. Markov’s constants of the corresponding set are evaluated.
Solvability Conditions for a Linearized Cahn-Hilliard Equation of Sixth Order
We obtain solvability conditions in H6(ℝ3) for a sixth order partial differential equation which is the linearized Cahn-Hilliard problem using the results derived for a Schrödinger type operator without Fredholm property in our preceding article [18].
Solvability of the Poisson equation in weighted Sobolev spaces
The aim of this paper is to prove the existence of solutions to the Poisson equation in weighted Sobolev spaces, where the weight is the distance to some distinguished axis, raised to a negative power. Therefore we are looking for solutions which vanish sufficiently fast near the axis. Such a result is useful in the proof of the existence of global regular solutions to the Navier-Stokes equations which are close to axially symmetric solutions.
Some applications of generalized condensers in the theory of analytic functions.
Some properties and characterizations of -normal functions.
Some properties of weighted hyperbolic polynomials.
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.
Superlinear CG convergence for special right-hand sides.