Related papers: The Bergman kernel for the Vekua equation

Transposing the Berezin quantization into the setting of analytic microlocal analysis, we construct approximate semiclassical Bergman projections on weighted $L^2$ spaces with analytic weights, and show that their kernel functions admit an…

We consider a certain Hartogs domain which is related to the Fock-Bargmann space. We give an explicit formula for the Bergman kernel of the domain in terms of the polylogarithm functions. Moreover we solve the Lu Qi-Keng problem of the…

We present an elementary proof for an approximate expression of the Bergman kernel on homogeneous spaces, and products of them. The error term is exponentially small with respect to the inverse semiclassical parameter.

We introduce the spaces $A^p_{\alpha, \beta}(\Omega)$ of $L^p$-solutions to the Vekua equation (generalized monogenic functions) $D w=\alpha\overline{w}+\beta w$ in a bounded domain in $\mathbb{R}^n$, where $D=\sum_{i=1}^n e_i \partial_i$…

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…

The purpose of this article is to study operators whose kernel share some key features of Bergman kernels from complex analysis, and are approximate projectors. It turns out that they must be associated with a rich set of geometric data, on…

In this paper we continue the study of Bergman theory for the class of slice regular functions. In the slice regular setting there are two possibilities to introduce the Bergman spaces, that are called of the first and of the second kind.…

In this paper we consider the reproducing kernel thesis for boundedness and compactness for various operators on Bergman-type spaces. In particular, the results in this paper apply to the weighted Bergman space on the unit ball, the unit…

We obtain ceratin estimates for the reproducing kernels of large weighted Bergman spaces. Applications of these estimates to boundedness of the Bergman projection on $L^p(\D,\omega ^{p/2})$, complex interpolation and duality of weighted…

In this paper, we prove the boundedness of the Bergman projection on weighted mixed norm spaces of the upper-half space for some weights that are constructed using the logarithm function and growth functions. Our necessary and sufficient…

In this note we verify certain statement about the operator $Q\_K$ constructed by Donaldson in [3] by using the full asymptotic expansion of Bergman kernel obtained in [2] and [4].

This note gives an explicit description of conditional measures for the determinantal point process with the Bergman kernel.

We obtain an asymptotic expansion and some regularity results for the Bergman kernel on the intersection of two balls in C^2.

We calculate the weighted Bergman kernel on a complex domain with a weight of the form $\rho=e^{-\alpha\phi}\mu g$, where $\alpha$ is a positive real number, $\phi$ is a K\"ahler potential, g is the determinant of the corresponding K\"ahler…

We find kernel functions of the $q$-Heun equation and its variants. We apply them to obtain $q$-integral transformations of solutions to the $q$-Heun equation and its variants. We discuss special solutions of the $q$-Heun equation from the…

We show how to compute the Bergman kernel functions of some special domains in a simple way. As an application of the explicit formulas, we show that the Bergman kernel functions of some convex domains, for instance the domain in C^3…

We describe a notion of ampleness for line bundles on orbifolds with cyclic quotient singularities that is related to embeddings in weighted projective space, and prove a global asymptotic expansion for a weighted Bergman kernel associated…

The transmutation (transformation) operator associated with the perturbed Bessel equation is considered. It is shown that its integral kernel can be uniformly approximated by linear combinations of constructed here generalized wave…

In this paper, we investigate a restricted version of Bergman kernels for high powers of a big line bundle over a smooth projective variety. The geometric meaning of the leading term is specified. As a byproduct, we derive some integral…

We~identify the standard weighted Bergman kernels of spaces of nearly holomorphic functions, in~the sense of Shimura, on~bounded symmetric domains. This also yields a description of the analogous kernels for spaces of…