Related papers: Lu Qi-Keng's Problem

We obtain a quantitative estimate of Bergman distance when $\Omega \subset \mathbb{C}^n$ is a bounded domain with log-hyperconvexity index $\alpha_l(\Omega)>\frac{n-1+\sqrt{(n-1)(n+3)}}{2}$, as well as the $A^2(\log A)^q$-integrability of…

This paper provides a precise asymptotic expansion for the Bergman kernel on the non-smooth worm domains of Christer Kiselman in complex 2-space. Applications are given to the failure of Condition R, to deviant boundary behavior of the…

I present a selection of conceptual and mathematical problems in the foundations of modern physics as they derive from the title question. Contribution to a panel session, "Springer Forum: Quantum Structures -- Physical, Mathematical and…

This report examines the open questions that remain unsolved following the measurements with antineutrons ($\bar n$) as probes conducted up to the 1990s at the LEAR facility at CERN. It also presents suggestions for possible new experiments…

On a two dimensional Stein space with isolated, normal singularities, smooth finite type boundary, and locally algebraic Bergman kernel, we establish an estimate on the type of the boundary in terms of the local algebraic degree of the…

In this paper we determine explicitly the kernels $\mathbb K_{\alpha,\beta}$ associated with new Bergman spaces $\mathcal A_{\alpha,\beta}^2(\mathbb D)$ considered recently by the first author and M. Zaway. Then we study the distribution of…

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,…

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…

There exist several interesting results in the literature on subnormal operator tuples having their spectral properties tied to the geometry of strictly pseudoconvex domains or to that of bounded symmetric domains in $\C^n$. We introduce a…

The purpose of this paper is to prove optimal estimates for solutions of the Kohn-Laplacian for certain classes of model domains in several complex variables. This will be achieved by applying a type of singular integral operator whose…

In earlier work the authors proved the Bergman kernel expansion for semipositive line bundles over a Riemann surface whose curvature vanishes to atmost finite order at each point. Here we explore the related results and consequences of the…

This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting. For a wide class of compact, connected $C^\infty$ Riemannian manifolds, including the important cases of spheres and…

Boundary Behaviour of Weighted Bergman Kernels: For a planar domain $D \subset \mathbb{C}$ and an admissible weight function $\mu$ on it, some aspects of the boundary behaviour of the corresponding weighted Bergman kernel $K_{D, \mu}$ are…

We obtain necessary and sufficient conditions for the $L^p$-boundedness of the operator with positive Bergman kernel in some homogeneous Siegel domains of Cn. The key tool used here is the Okikiolu test, which finally leads to better result…

In this note, it is shown that the differential polynomial of the form $Q(f)^{(k)}-p$ has infinitely many zeros, and particularly $Q(f)^{(k)}$ has infinitely many fixed points for any positive integer $k$, where $f$ is a transcendental…

The goal of this note is to explore the Bergman projection on forms. In particular, we show that some of most basic facts used to construct the Bergman kernel on functions, such as pointwise evaluation in…

In this paper we consider the zeros of the Bergman kernel of the Fock-Bargmann-Hartogs domain $D_{n,m}$. We describe how the existence of zeros of the Bergman kernel depends on the integers $m$ and $n$ with the help of the interlacing…

In this paper we investigate the Bergman kernel function for intersection of two complex ellipsoids $\{(z,w_1,w_2) \in \mathbb{C}^{n+2} : |z_1|^2 + \cdots + |z_n|^2 + |w_1|^q < 1, \quad |z_1|^2 + \cdots + |z_n|^2 + |w_2|^r < 1\}.$

In our preprint q-alg/9703005 q-analogues of bounded symmetric domains were defined to be homogeneous spaces of the associated quantum groups. The investigation of a simplest among those domains, the quantum matrix ball, was started in…

We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain $\Omega$ of a rectangular domain $I\times I$ to a covariance kernel on the entire domain $I\times I$. For a…