The Poisson Boundary of the Mapping Class Group and of Teichmüller Space
The Poisson formula for groups with hyperbolic properties.
The Poisson integral for a ball in spaces of constant curvature
We present explicit expressions of the Poisson kernels for geodesic balls in the higher dimensional spheres and real hyperbolic spaces. As a consequence, the Dirichlet problem for the projective space is explicitly solved. Comparison of different expressions for the same Poisson kernel lead to interesting identities concerning special functions.
The Poisson Space of the Koranyi Ball.
The Poisson summation formula for a Dirichlet problem with gliding and glancing rays
The resolvent for a convolution kernel satisfying the domination principle
The restriction theorem for fully nonlinear subequations
Let be a submanifold of a manifold . We address the question: When do viscosity subsolutions of a fully nonlinear PDE on , restrict to be viscosity subsolutions of the restricted subequation on ? This is not always true, and conditions are required. We first prove a basic result which, in theory, can be applied to any subequation. Then two definitive results are obtained. The first applies to any “geometrically defined” subequation, and the second to any subequation which can be transformed...
The Schur harmonic convexity of the Hamy symmetric function and its applications.
The surjectivity of a constant coefficient homogeneous differential operator in the real analytic functions and the geometry of its symbol
Hörmander has characterized the surjective constant coefficient partial differential operators on the space of all real analytic functions on by a Phragmén-Lindelöf condition. Geometric implications of this condition and, for homogeneous operators, of the corresponding condition for Gevrey classes are given.
The symmetric pluricomplex Green function
The trilinear embedding theorem
Let , i = 1,2,3, denote positive Borel measures on ℝⁿ, let denote the usual collection of dyadic cubes in ℝⁿ and let K: → [0,∞) be a map. We give a characterization of a trilinear embedding theorem, that is, of the inequality in terms of a discrete Wolff potential and Sawyer’s checking condition, when 1 < p₁,p₂,p₃ < ∞ and 1/p₁ + 1/p₂ + 1/p₃ ≥ 1.
The uniform norming of retractions on short intervals for certain function spaces.
The upper bound of the number of eigenvalues for a class of perturbed Dirichlet forms
The theory of Markov processes and the analysis on Lie groups are used to study the eigenvalue asymptotics of Dirichlet forms perturbed by scalar potentials.
The Wiener Type Solution of the Dirichlet Problem in Potential Theory.
The Wolff gradient bound for degenerate parabolic equations
The spatial gradient of solutions to non-homogeneous and degenerate parabolic equations of -Laplacean type can be pointwise estimated by natural Wolff potentials of the right hand side measure.
Théorie des processus de production
Théorie du potentiel associée à certains systèmes différentiels.
Theory of Bessel potentials. III : potentials on regular manifolds
In this paper Bessel potentials on -Riemannian manifolds (open or bordered) are studied. Let be an -dimensional manifold, and a submanifold of of dimension . Sufficient conditions are given for: 1) the restriction to of any potential of order on to be a potential of order on ; 2) any potential of order on to be extendable to a potential of order on . It is also proved that for a bordered manifold the restriction to its interior is an isometric isomorphism between the...
Thinness and non-tangential limit associated to coupled PDE
In this paper, we study the reduit, the thinness and the non-tangential limit associated to a harmonic structure given by coupled partial differential equations. In particular, we obtain such results for biharmonic equation (i.e. ) and equations of type.
Topologie fine dans les espaces harmoniques