Related papers: Multivariable isometries related to certain convex…

We show that a smooth bounded domain in $\mathbb{C}^n$ admitting partial pseudoconvex exhaustion remains partial pseudoconvex. The main ingredient of the proof is based on a new characterization of hyper-$q$-convex domains. Furthermore, we…

Let $\Omega$ be a bounded domain in $\mathbb R^2$ with smooth boundary $\partial\Omega$, and let $\omega_h$ be the set of points in $\Omega$ whose distance from the boundary is smaller than $h$. We prove that the eigenvalues of the…

Linear spaces with an Euclidean metric are ubiquitous in mathematics, arising both from quadratic forms and inner products. Operators on such spaces also occur naturally. In recent years, the study of multivariate operator theory has made…

In this work we consider higher dimensional thin domains with the property that both boundaries, bottom and top, present oscillations of weak type. We consider the Laplace operator with Neumann boundary conditions and analyze the behavior…

We show that Property $(P)$ of $\partial\Omega$, compactness of the $\bar{\partial}$-Neumann operators $N_1$, and compactness of Hankel operator on a smooth bounded pseudoconvex Hartogs domain $\Omega={\{(z, w_1, w_2,\dots, w_n) \in…

We shall give a definition of the curvature operator for a family of weighted Bergman spaces $\{\mathcal H_t\}$ associated to a smooth family of smoothly bounded strongly pseudoconvex domains $\{D_t\}$. In order to study the boundary term…

We derive optimal estimates for the Bergman kernel and the Bergman metric for certain model domains in $\mathbb{C}^2$ near boundary points that are of infinite type. Being unbounded models, these domains obey certain geometric constraints…

We study some special almost complex structures on strictly pseudoconvex domains. They appear naturally as limits under a nonisotroping scaling procedure and play a role of model objects in the geometry of almost complex manifolds with…

Let $\Omega\subset \mathbb{C}^2$ be a bounded pseudoconvex complete Reinhardt domain with a smooth boundary. We study the behavior of analytic structure in the boundary of $\Omega$ and obtain a compactness result for Hankel operators on the…

By establishing a unified estimate of the twisted Kohn-Morrey-H\"{o}rmander estimate and the $q$-pseudoconvex Ahn-Zampieri estimate, we discuss variants of Property $(P_q)$ of Catlin and Property $(\widetilde{P_q})$ of McNeal on the…

We characterize Hilbert-Schmidt Hankel operators on the Bergman spaces of smooth bounded strongly pseudoconvex domains in $\mathbb{C}^n$ for $n \geq 2$. We consider harmonic symbols of class $C^3$ up to the closure of the domain and show…

An analysis of the boundary representations and C$^*$-envelopes of some finite-dimensional operator systems $\mathcal R$ is undertaken by considering relationships between operator-theoretic properties of a $d$-tuple $\mathfrak…

We review recent interactions between mathematical theory of two-dimensional topological order and operator algebras, particularly the Jones theory of subfactors. The role of representation theory in terms of tensor categories is…

In this paper we prove discreteness of the spectrum of the Neu\-mann-Lap\-la\-ci\-an (the free membrane problem) in a large class of non-convex space domains. The lower estimates of the first non-trivial eigenvalue are obtained in terms of…

Let $\Omega$ be a strongly pseudoconvex domain. We introduce the Mabuchi space of strongly plurisubharmonic functions in $\Omega$. We study metric properties of this space using Mabuchi geodesics and establish regularity properties of the…

We introduce a new class of integral domains, the perinormal domains, which fall strictly between Krull domains and weakly normal domains. We establish basic properties of the class, and in the case of universally catenary domains we give…

We shall give a variational formula of the full Bergman kernels associated to a family of smoothly bounded strongly pseudoconvex domains. An equivalent criterion for the triviality of holomorphic motions of planar domains in terms of the…

We study spectral properties of divergence form elliptic operators $-\textrm{div} [A(z) \nabla f(z)]$ with the Neumann boundary condition in planar domains (including some fractal type domains), that satisfy to the quasihyperbolic boundary…

This paper mainly concerns the von Neumann algebras induced by a tuple of multiplication operators on Bergman spaces which arise essentially from holomorphic proper maps over higher dimensional domains. We study the structures and abelian…

Given a Schr\"odinger operator with a real-valued potential on a bounded, convex domain or a bounded interval we prove inequalities between the eigenvalues corresponding to Neumann and Dirichlet boundary conditions, respectively. The…