Related papers: A Tale of Three Kernels

We study properties of weighted Szeg\H{o} and Garabedian kernels on planar domains. Motivated by the unweighted case as explained in Bell's work, the starting point is a weighted Kerzman-Stein formula that yields boundary smoothness of the…

The quotient of the Szeg\"{o} and Bergman kernels for a smooth bounded pseudoconvex domains in ${\mathbb C}^n$ is bounded from above by $\delta|\log\delta|^p$ for any $p>n$, where $\delta$ is the distance to the boundary. For a class of…

We describe the Szeg\"o kernel on a higher genus Riemann surface in terms of Szeg\"o kernel data coming from lower genus surfaces via two explicit sewing procedures where either two Riemann surfaces are sewn together or a handle is sewn to…

Very recently one has started to study Bergman and Szeg\"o kernels in the setting of octonionic monogenic functions. In particular, explicit formulas for the Bergman kernel for the octonionic unit ball and for the octonionic right…

Actually we will discuss some topics related to Bergman kernel on Cartan- Hartogs domain.

We show that the Bergman, Szego, and Poisson kernels associated to a finitely connected domain in the plane are all composed of finitely many easily computed functions of one variable. The new formulas give rise to new methods for computing…

We use Stokes's theorem to establish an explicit and concrete connection between the Bergman and Szeg\H{o} projections on the disc, the ball, and on strongly pseudoconvex domains.

We consider the Szeg\"o kernel for domains \Omega in C^2 given by \Omega = {(z,w): Im w > b(Re z)} where b is a non-convex quartic polynomial with positive leading coefficient. Such domains are not pseudoconvex. We describe the subset of…

We prove optimal estimates of the Bergman and Szeg\H{o} kernels on the diagonal, and the Bergman metric near the boundary of bounded smooth generalized decoupled pseudoconvex domains in $\mathbb{C}^n$. The generalized decoupled domains we…

No abstract available.

We generalize Nagel's formula for the Szeg\"o kernel and use it to compute the Szeg\"o kernel on a class of noncompact CR manifolds whose tangent space decomposes into one complex direction and several totally real directions. We also…

We explore the relationship between the Bergman kernel of a Hartogs domain and weighted Bergman kernels over its base domain. In particular we develop a representation of the Bergman kernel of a Hartogs domain as a series involving weighted…

We consider the Szeg\"o kernel for non-pseudoconvex domains in C^2 given by \Omega = {(z,w): Im w > b(Re z)} for b a non-convex even-degree polynomial with positive leading coefficient. This is an extension of results previously obtained by…

Let $\{\Omega_t:-1<t<1\}$ be a family of bounded pseudoconvex domains and $\varphi_t\in PSH(\Omega_t)$. Let $K_t(z,w)$ denote the Bergman kernel with weight $\varphi_t$ on $\Omega_t$. We study the continuity and H\"older continuity of…

In a digraph, a kernel is a subset of vertices that is both independent and absorbing. Kernels have important applications in combinatorics and outside. Kernels do not always exist and finding sufficient conditions ensuring their existence…

The Bergman theory of domains $\{ |{z_{1} |^{\gamma}} < |{z_{2}} | < 1 \}$ in $\mathbb{C}^2$ is studied for certain values of $\gamma$, including all positive integers. For such $\gamma$, we obtain a closed form expression for the Bergman…

Quarks, leptons and heavy vector bosons are suggested to be composed of stable spin-1/2 preons, existing in three flavours, combined according to simple rules. Straightforward consequences of an SU(3) preon-flavour symmetry are 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…

In a previous article by two of the present authors and S. Bonzio, \L ukasiewicz near semirings were introduced and it was proven that basic algebras can be represented (precisely, are term equivalent to) as near semirings. In the same work…

This is our third work on Bergman-type operator over bounded domains. In the previous two articles, we systematically study the boundedness, compactness and Schatten membership of Bergman-type on the Hilbert unit ball. In the present paper,…