Related papers: Convergence speed of weighted Bergman kernels towa…

Consider a complex line bundle over a compact complex manifold equipped with an infinitely differentiable metric with strictly positive curvature form. Assign to positive tensor powers of this bundle the associated product metrics and…

In this article we present a Bernstein inequality for sums of random variables which are defined on a graphical network whose nodes grow at an exponential rate. The inequality can be used to derive concentration inequalities in…

Let $\Omega$ be a convex domain in $\mathbb{C}^n$ and $\varphi$ a convex function on $\Omega$. We prove that $\log{K_{\Omega,\varphi}(z)}$ is a convex function (might be identically $-\infty$) on $\Omega$, where $K_{\Omega,\varphi}$ is the…

Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the…

In this article, we study some properties of the $n$-th order weighted reduced Bergman kernels for planar domains, $n\geq 1$. Specifically, we look at Ramadanov type theorems, localization, and boundary behaviour of the weighted reduced…

For a general adapted integrable right-continuous with left limits (RCLL) process $(X_t)_{t\in[0,\tau]}$ taking values in a metric space $(\mathcal E,d)$, we show (among other things) that for every $m\in(1,\infty)$ $$…

Consider a stationary, linear Hilbert space valued process. We establish Berry-Essen type results with optimal convergence rates under sharp dependence conditions on the underlying coefficient sequence of the linear operators. The case of…

Let G be a bounded Jordan domain in the complex plane with piecewise analytic boundary. We present theoretical estimates and numerical evidence for certain phenomena, regarding the application of the Bergman kernel method with algebraic and…

Given a sequence of regular planar domains converging in the sense of kernel, we prove that the corresponding Green's functions converge uniformly on the complex sphere, provided the limit domain is also regular, and the connectivity is…

In a previous paper, \cite{Berndtsson}, we have studied a property of subharmonic dependence on a parameter of Bergman kernels for a family of weighted $L^2$-spaces of holomorphic functions. Here we prove a result on the curvature of a…

Let $V$ be a symmetric convex body in $\R^m$. We prove sharp Bernstein-type inequalities for entire functions of exponential type with the spectrum in $V$ and discuss certain properties of the extremal functions. Markov-type inequalities…

We consider the weighted Bergman space $A^2_\psi(\Bn)$ of all holomorphic functions on $\Bn$ square integrable with respect to a particular exponential weight measure $e^{-{\psi}} dV$ on $\Bn$, where \begin{align*}…

In this article, we introduce a kernel-based consensual aggregation method for regression problems. We aim to flexibly combine individual regression estimators $r_1, r_2, \ldots, r_M$ using a weighted average where the weights are defined…

Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for…

We introduce another new type of combinations of Bernstein operators in this paper, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type…

The first aim of the present note is to quantify the speed of convergence of a conditioned process toward its Q-process under suitable assumptions on the quasi-stationary distribution of the process. Conversely, we prove that, if a…

We provide a counterexample to the Sarason Conjecture for the Bergman space and present a characterisation of bounded Toeplitz products on the Bergman space in terms of test functions by means of a dyadic model approach. We also present…

We consider the existence and uniqueness of a minimizer of the extremal problem for weighted combined energy between two concentric annuli and obtain that the extremal mapping is a certain radial mapping. Meanwhile, this in turn implies a…

The inequality of Berwald is a reverse-H\"older like inequality for the $p$th average, $p\in (-1,\infty),$ of a non-negative, concave function over a convex body in $\mathbb{R}^n.$ We prove Berwald's inequality for averages of functions…

For any open hyperbolic Riemann surface $X$, the Bergman kernel $K$, the logarithmic capacity $c_{\beta}$, and the analytic capacity $c_{B}$ satisfy the inequality chain $\pi K \geq c^2_{\beta} \geq c^2_B$; moreover, equality holds at a…