Related papers: Parameter dependence of the Bergman kernels

Let $K$ be a p.c.f. self-similar set equipped with a strongly recurrent Dirichlet form. Under a homogeneity assumption, for an open set $\Omega\subset K$ whose boundary $\partial \Omega$ is a graph-directed self-similar set, we prove that…

We derive optimal estimates for the Bergman kernel and the Bergman metric for certain model domains in $\mathbb{C}^2$ near boundary points that are of infinite type. Being unbounded models, these domains obey certain geometric constraints…

Motivated by recent work on strict deformation quantization of the unit disk and the Riemann sphere, we study the Fr\'echet space structure of the set of holomorphic functions on the complement $\Omega:=\{(z,w)\in \hat{\mathbb{C}}^2\, :\,…

We investigate some spectral properties of the weighted quaternionic Cauchy transform when acting on the right quaternionic Hilbert space of Gaussian integrable functions. We study its boundedness, compactness, and memberships to the…

Let $D$ be a bounded strongly convex domain in the complex space of dimension $n$. Fixed a point $p\in \partial D$, we consider the solution of a homogeneous complex Monge-Ampere equation with simple pole at $p$. We prove that such a…

In this paper we study skew Poincar\'e-Birkhoff-Witt extensions over weak symmetric and $(\Sigma,\Delta)$-weak symmetry rings. Since these extensions generalize Ore extensions of injective type and another noncommutative rings of polynomial…

Let $D$ be a bounded strictly pseudoconvex domain in $\mathbb{C}^n$. Assuming $bD \in C^{k+3+\alpha}$ where $k$ is a non-negative integer and $0 < \alpha \leq 1$, we show that 1) the Bergman kernel $B(\cdot, w_0) \in C^{k+ \min\{\alpha,…

The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson structures obtained from a generalized Adler map in the space of formal pseudodifferential symbols with noninteger powers. The resulting $\W$-algebra is a…

Let $K: \boldsymbol{\Omega}\times \boldsymbol{\Omega}$ be a continuous Mercer kernel defined on a compact subset of ${\mathbb R}^n$ and $\mathcal{H}_K$ be the reproducing kernel Hilbert space (RKHS) associated with $K$. Given a finite…

Highly localized kernels constructed by orthogonal polynomials have been fundamental in recent development of approximation and computational analysis on the unit sphere, unit ball and several other regular domains. In this work we first…

We study a class of weight functions on $[-1,1]$, which are special cases of the general weights studied by Bernstein and Szeg\"o, as well as their extentions to the interval $[-a,1]$ for a continuous parameter $a>0$. These weights are…

We develop geometry of algebraic subvarieties of $K^{n}$ over arbitrary Henselian valued fields $K$. This is a continuation of our previous article concerned with algebraic geometry over rank one valued fields. At the center of our approach…

We show that on smooth complete Reinhardt domains, weighted Bergman projection operators corresponding to exponentially decaying weights are unbounded on $L^p$ spaces for all $p\not=2$. On the other hand, we also show that the exponentially…

We establish the convexity of Mabuchi's K-energy functional along weak geodesics in the space of Kahler potentials on a compact Kahler manifold thus confirming a conjecture of Chen and give some applications in Kahler geometry, including a…

Consider a Lipschitz domain $\Omega$ and the Beurling transform of its characteristic function $\mathcal{B} \chi_\Omega(z)= - {\rm p.v.}\frac1{\pi z^2}*\chi_\Omega (z) $. It is shown that if the outward unit normal vector $N$ of the…

For a class of $O(n+1,R)$ invariant measures on the Kepler manifold possessing finite moments of all orders, we describe the reproducing kernels of the associated Bergman spaces, discuss the corresponding asymptotic expansions of…

We consider an eigenvalue problem of the form \begin{equation*} \left\{\begin{array}{rclll} -\Delta_{p} u -\Delta_{q} u&=& \lambda K(x)|u|^{p-2}u & \mbox{ in } \Omega^e u&=&0\qquad \quad &\mbox{ on } \partial \Omega u(x) &\to& 0 &\mbox{ as…

We study integral kernels of strongly continuous semigroups on Lebesgue spaces over metric measure spaces. Based on semigroup smoothing properties and abstract Morrey-type inequalities, we give sufficient conditions for H\"older or…

We present a framework for reconstructing any simply connected, bounded or unbounded, quadrature domain $\Omega$ from its quadrature function $h$. Using the Faber transform, we derive formulae directly relating $h$ to the Riemann map for…

The existence of quasi-bi-Hamiltonian structures for a two-dimensional superintegrable $(k_1,k_2,k_3)$-dependent Kepler-related problem is studied. We make use of an approach that is related with the existence of some complex functions…