On a theorem of Cartan
On a theorem of M. G. Arsove
On a theorem of M. Itô
The note gives a simple proof of a result of M. Itô, stating that the set of divisors of a convolution kernel is a convex cone.
On a version of Littlewood-Paley function
On absorption times and Dirichlet eigenvalues
This paper gives a stochastic representation in spectral terms for the absorption time T of a finite Markov chain which is irreducible and reversible outside the absorbing point. This yields quantitative informations on the parameters of a similar representation due to O'Cinneide for general chains admitting real eigenvalues. In the discrete time setting, if the underlying Dirichlet eigenvalues (namely the eigenvalues of the Markov transition operator restricted to the functions vanishing on...
On an extension of jump-type symmetric Dirichlet forms.
On an extension of the definition of transfinite diameter and some applications.
On approach regions for the conjugate Poisson integral and singular integrals
Let ũ denote the conjugate Poisson integral of a function . We give conditions on a region Ω so that , the Hilbert transform of f at x, for a.e. x. We also consider more general Calderón-Zygmund singular integrals and give conditions on a set Ω so that is a bounded operator on , 1 < p < ∞, and is weak (1,1).
On Boundary Behaviour of Harmonic Functions in Hölder Domains.
On boundary Harnack principles and poles of extremal harmonic functions.
On boundary integral equations of the first kind for the bi-laplacian in a polygonal plane domain
On Brownian and Poissonian Convolution Semigroups on the Infinite Dimensional Torus
On certain harmonic measures on the unit disk
On certain oscillatory properties for solutions of an equation with a biharmonic leading part
On certain p-harmonic functions in the plane.
On certain reflexion principes
On coincidence of p-module of a family of curves and p-capacity on the Carnot group.
The notion of the extremal length and the module of families of curves has been studied extensively and has given rise to a lot of applications to complex analysis and the potential theory. In particular, the coincidence of the p-module and the p-capacity plays an mportant role. We consider this problem on the Carnot group. The Carnot group G is a simply connected nilpotent Lie group equipped vith an appropriate family of dilations. Let omega be a bounded domain on G and Ko, K1 be disjoint non-empty...
On convergence sets of divergent power series
A nonlinear generalization of convergence sets of formal power series, in the sense of Abhyankar-Moh [J. Reine Angew. Math. 241 (1970)], is introduced. Given a family of analytic curves in ℂ × ℂⁿ passing through the origin, of a formal power series f(y,t,x) ∈ ℂ[[y,t,x]] is defined to be the set of all s ∈ ℂ for which the power series converges as a series in (t,x). We prove that for a subset E ⊂ ℂ there exists a divergent formal power series f(y,t,x) ∈ ℂ[[y,t,x]] such that if and only if...
On critical points of harmonic functions in the plane.
On cyclic and radial variations of a plane path (Preliminary communication)