Simplicial Cones in Potential Theory II (Approxiamtion Theorems).
Singular and Quasi-Bounded Functions Associated with the Heat Equation.
Singular behavior of conformal Martin kernels and non-tangential limits of conformal mappings.
Singular functions on metric measure spaces.
On relatively compact domains in metric measure spaces we construct singular functions that play the role of Green functions of the p-Laplacian. We give a characterization of metric spaces that support a global version of such singular function, in terms of capacity estimates at infinity of such metric spaces. In addition, when the measure of the space is locally Q-regular, we study quasiconformal invariance property associated with the existence of global singular functions.
Singular sets of separately analytic functions
We complete the characterization of singular sets of separately analytic functions. In the case of functions of two variables this was earlier done by J. Saint Raymond and J. Siciak.
Singularité et intégrabilité des fonctions plurisousharmoniques
On étudie les singularités et l’intégrabilité d’une classe de fonctions plurisousharmoniques sur une variété analytique de dimension . Pour étudier ce problème, nous commençons par contrôler les nombres de Lelong de certains types de fonctions plurisousharmoniques . Ensuite, nous étudions les singularités du transformé strict du courant par un éclatement de au dessus d’un point. Nous répondons ainsi positivement au problème d’intégrabilité locale de , lorsque , et lorsque est une fonction plurisousharmonique...
Singularités des fonctions de Green hypoelliptiques
Singularity of parabolic measures
Slow growth for universal harmonic functions.
Slowly growing subharmonic function II.
Slowly growing subharmonic functions I.
Smale's Conjecture on Mean Values of Polynomials and Electrostatics
2000 Mathematics Subject Classification: Primary 30C10, 30C15, 31B35.A challenging conjecture of Stephen Smale on geometry of polynomials is under discussion. We consider an interpretation which turns out to be an interesting problem on equilibrium of an electrostatic field that obeys the law of the logarithmic potential. This interplay allows us to study the quantities that appear in Smale’s conjecture for polynomials whose zeros belong to certain specific regions. A conjecture concerning the electrostatic equilibrium...
Small sets in
Small values of polynomials: Cartan, Pólya and others.
Small-time asymptotic estimates in local Dirichlet spaces.
Smooth, but not Complex-Analytic Pluripolar Sets.
Smooth potentials with prescribed boundary behaviour.
This paper examines when it is possible to find a smooth potential on a C1 domain D with prescribed normal derivatives at the boundary. It is shown that this is always possible when D is a Liapunov-Dini domain, and this restriction on D is essential. An application concerning C1 superharmonic extension is given.
Smoothing Plurisubharmonic Functions on Complex Spaces.
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.