Related papers: Boundary singularity of Poisson and harmonic Bergm…

The main purpose of this article is to explore the possibility of extending the notion of peripheral Poisson boundary of unital completely positive (UCP) maps to contractive completely positive (CCP) maps and to unital and non-unital…

For conformal boundary operators associated with the Paneitz operator, we introduce a rigorous definition of the biharmonic Poisson kernel consisting of a pair of kernel functions and derive its explicit representation formula. With this…

In this paper, we study the computational question of whether the Steklov spectrum of smooth simply connected planar domains can be approximated accurately by a boundary-only formulation based on harmonic conjugation. For the unit disk, the…

In this article, we introduce higher order conjugate Poisson and Poisson kernels, which are higher order analogues of the classical conjugate Poisson and Poisson kernels, as well as the polyharmonic fundamental solutions, and define…

Our main result introduces a new way to characterize two-dimensional finite ball quotients by algebraicity of their Bergman kernels. This characterization is particular to dimension two and fails in higher dimensions, as is illustrated by a…

Using an integral formula on a homogeneous Siegel domain, we show a necessary and sufficient condition for composition operators on the weighted Bergman space of a minimal bounded homogeneous domain to be compact. To describe the…

We contruct two classes of Zalcman-type domains, on which the Bergman distance functions have certain pre-described boundary behaviors. Such examples also lead to generalizations of uniformly perfectness in the sense of Pommerenke. These…

We describe recent work on the Bergman kernel of the (non-smooth) worm domain in several complex variables. An asymptotic expansion is obtained for the Bergman kernel. Mapping properties of the Bergman projection are studied. Irregularity…

Let X be a strictly pseudoconcave domain in a closed polarized complex manifold (Y,L) where L is a (semi-)positive line bundle over Y. Any given Hermitian metric on L, together with a volume form, induces by restriction to X a Hilbert space…

In this article, we explore the boundedness properties of pseudo-differential operators on radial sections of line bundles over the Poincar\'e upper half plane, even when dealing with symbols of limited regularity. We first prove the…

One of the basic aims of this paper is to study the relationship between the geometry of ``hypersurface like'' subsets of Euclidean space and the properties of the measures they support. In this context we show that certain doubling…

For a class of non-selfadjoint semiclassical operators in dimension one, we get a complete asymptotic description of all eigenvalues near a critical value of the leading symbol of the operator on the boundary of the pseudospectrum.

In this note, we prove a theorem \`a la Fatou for the square root of Poisson Kernel in the context of quasi-convex cocompact discrete groups of isometries of $\delta$-hyperbolic spaces. As a corollary we show that some matrix coefficients…

Let $\Omega\subset \mathbb{C}^n$ for $n\geq 2$ be a bounded pseudoconvex domain with a $C^2$-smooth boundary. We study the compactness of composition operators on the Bergman spaces of smoothly bounded convex domains. We give a partial…

In a previous paper, we studied a kernel estimate of the upper edge of a two-dimensional bounded set, based upon the extreme values of a Poisson point process. The initial paper "Geffroy J. (1964) Sur un probl\`eme d'estimation…

Let $M$ be an $n$-dimensional Hadamard manifold of pinched negative curvature $-b^2 \leq K_M \leq -a^2$. The solution of the Dirichlet problem at infinity for $M$ leads to the construction of a family of mutually absolutely continuous…

This paper develops a new Hilbert space method to characterize a family of reproducing kernel Hilbert spaces of real harmonic functions in a bounded Lipschitz domain $\Omega \subset \mathbb R^d, d\geq 2$ involving some families of positive…

We study the boundary layer solution to singular perturbation problems involving Poisson-Boltzmann (PB) type equations with a small parameter $\epsilon$ in general bounded smooth domains (including multiply connected domains) under the…

Motivated by the study of kernels of bilinear pseudodifferential operators with symbols in a H\"ormander class of critical order, we investigate boundedness properties of strongly singular Calder\'on--Zygmund operators in the bilinear…

We obtain a conceptually new differential geometric proof of P.F. Klembeck's result that the holomorphic sectional curvature of a strictly pseudoconvex domain approaches (in the boundary limit) the constant sectional curvature of the…