Related papers: A Tale of Three Kernels

A known property of conditional expectation is extended to the framework of Markov kernels. Its meaning in terms of densities is provided. Some examples located in the field of clinical diagnosis are presented to delimit the main result of…

A compsite model of quarks and leptons is proposed. The quarks and leptons are given by three body states which are composed of constituents $(w_1, w_2, c_1, c_2, c_3)$ of SU(5)$_{flavor}$ and $(f_1, f_2, f_3)$ of SU(3)$_{family}$

We consider mixed normed Bergman spaces on homogeneous Siegel domains. In the literature, two different approaches have been considered and several results seem difficult to be compared. In this paper we compare the results available in the…

We obtain the octonionic Bergman kernel for half space in the octonionic analysis setting by two different methods. As a consequence, we unify the kernel forms in both complex analysis and hyper-complex analysis.

We obtain new explicit formulas for the Bergman kernel function on two families of Hartogs domains. To do so, we first compute the Bergman kernels on the slices of these Hartogs domains with some coordinates fixed, evaluate these kernel…

A streamlined proof that the Bergman kernel associated to a quadrature domain in the plane must be algebraic will be given. A byproduct of the proof will be that the Bergman kernel is a rational function of z and one other explicit function…

In this paper, we study the kernels of the $\mathrm{SO}(3)$-Witten-Reshetikhin-Turaev quantum representations $\rho_p$ of mapping class groups of closed orientable surfaces $\Sigma_g$ of genus $g.$ We investigate the question whether the…

In this paper, we prove a property of kernels of Brauer characters. We propose a candidate for the kernels of Isaacs' partial characters, and we show that this candidate has the same property.

We introduce two classes of "egg type" domains, built on general bounded symmetric domains, for which we compute the Bergmann kernel in explicit form. We use the characterization of bounded symmetric domains through Jordan triple systems.…

We introduce the notion of "virtual Bergman kernel" and apply it to the computation of the Bergman kernel of "domains inflated by Hermitian balls", in particular when the base domain is a bounded symmetric domain.

We construct a family of representations of an arbitrary variant $S_a$ of a semigroup $S$, induced by a given representation of $S$, and investigate properties of such representations and their kernels.

We provide a potential theoretic characterization of vanishing chord-arc domains under minimal assumptions. In particular we show that, if a domain has Ahlfors regular boundary, the oscillation of the logarithm of the interior and exterior…

In this paper, we investigate the trigonometric Heckman-Opdam polynomials of type $A_1$. We establish connections with ultraspherical polynomials and derive an explicit expression for the associated Poisson kernel. Using the product…

We prove the kernel estimates related to subordinated semigroups on homogeneous trees. We study the long time propagation problem. We exploit this to show exit time estimates for (large) balls. We use an abstract setting of metric measure…

In this article we shall study the analytic theory and the representation theoretic interpretations of Hankel transforms and fundamental Bessel kernels of an arbitrary rank over an archimedean field.

In this paper, we develop the theory of weighted Bergman space and obtain a general representation formula of the Bergman kernel function for the spaces on the Reinhardt domain containing the origin. As applications, we calculate the…

For $g\geq 2$, let $\Gamma\subset\mathrm{Sp}(2g,\mathbb{R})$ be a discrete subgroup, which is either a cocompact subgroup or an arithmetic subgroup without torsion elements, and let $\mathbb{H}_{g}$ denote the Siegel upper half space of…

We give a complete description of the boundary behaviour of the Poisson kernel and the harmonic Bergman kernel of a bounded domain with smooth boundary, which in some sense is an analogue of the similar description for the usual Bergman…

In this paper we continue to investigate a certain class of Hankel-like positive definite kernels using their associated orthogonal polynomials. The main result of this paper is about the structure of this kind of kernels.

We consider a class of domains, generalizing the upper half-plane, and admitting rotational, translational and scaling symmetries, analogous to the half-plane. We prove Paley-Wiener type representations of functions in Bergman spaces of…