Related papers: A note on plurisubharmonic defining functions in $…

We establish a general uniqueness theorem for subharmonic functions of several variables on a domain. A corollary from this uniqueness theorem for holomorphic functions is formulated in terms of the zero subset of holomorphic functions and…

We consider overdetermined problems related to the fractional capacity. In particular we study $s$-harmonic functions defined in unbounded exterior sets or in bounded annular sets, and having a level set parallel to the boundary. We first…

Given a negative plurisubharmonic function $\phi$ in a bounded pseudoconvex domain of ${\mathbb C}^n$, we introduce and study its residual function $g_\phi$ determined by the asymptotic behavior of $\phi$ near its singularity points, both…

In order to study the Toeplitz algebras related to a Dirac operators in a neighborhood of a closed bounded domain D with smooth boundary in C^n we introduce a singular Cauchy type integral. We compute its principal symbol, thus initiating…

We give a local characterization of the class of functions having positive distributional derivative with respect to $\bar{z}$ that are almost everywhere equal to one of finitely many analytic functions and satisfy some mild non-degeneracy…

We revisit the phenomenon where, for certain domains $D$, if the squeezing function $s_D$ extends continuously to a point $p\in \partial{D}$ with value $1$, then $\partial{D}$ is strongly pseudoconvex around $p$. In $\mathbb{C}^2$, we…

Let $H$ be a separable Hilbert space, $A_c:\mathcal D_c\subset H\to H$ a densely defined unbounded operator, bounded from below, let $\mathcal D_{\min}$ be the domain of the closure of $A_c$ and $\mathcal D_{\max}$ that of the adjoint.…

For $D$, $D'$ analytic polyhedra in $C^n$, it is proven that a biholomorphic mapping $f\colon D\to D'$ extends holomorphically to a dense boundary subset under certain condition of general position. This result is also extended to a more…

Let A be a closed polar subset of a domain D in the complex plane C. We give a complete description of the pluripolar hull in D X C of the graph of a holomorphic function defined on D A. To achieve this, we prove for pluriharmonic measure…

We prove that every bounded finely plurisubharmonic function can be locally (in the pluri-fine topology) written as the difference of two usual plurisubharmonic functions. As a consequence finely plurisubharmonic functions are continuous…

The behavior of solutions to the biharmonic equation is well-understood in smooth domains. In the past two decades substantial progress has also been made for the polyhedral domains and domains with Lipschitz boundaries. However, very…

We use functions of a bicomplex variable to unify the existing constructions of harmonic morphisms from a 3-dimensional Euclidean or pseudo-Euclidean space to a Riemannian or Lorentzian surface. This is done by using the notion of…

In this paper we prove that bounded Hua-harmonic functions on tube domains that satisfy some boundary regularity condition are necessarily pluriharmonic. In doing so, we show that a similar theorem is true on one-dimensional extensions of…

We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $\alpha$, with $0<\alpha<1$, in the vicinity of an exceptional boundary point where all such functions…

In this paper we are concerned with the problem of local and global subextensions of (quasi-)plurisubharmonic functions from a "regular" subdomain of a compact K\"ahler manifold. We prove that a precise bound on the complex Monge-Amp\`ere…

We extend holomorphically polyharmonic functions on a real ball to a complex set being the union of rotated balls. We solve a Dirichlet type problem for complex polyharmonic functions with the boundary condition given on the union of…

It is shown that a smooth n dimensional manifold with a boundary in R^n admits a Boolean representation in terms of closed half spaces defined by the tangent hyperplanes at the points on its boundary. A similar result is established for…

Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…

We remove the local boundedness for $\mathscr{E}_{\alpha}$-subharmonicity in the framework of (not necessarily strongly local) regular symmetric Dirichlet form $(\mathscr{E},D(\mathscr{E}))$ with $\alpha\geq0$ and establish the stochastic…

1.An expression for the smoothed counting function in terms of the fractional derivatives of the delta-function is presented. 2. The Neumann-Dirichlet (ND) boundary problem is introduced via some elementary examples based on a functorial…