Related papers: Dirichlet-like space and capacity in complex analy…

We consider an energy functional combining the square of the local oscillation of a one--dimensional function with a double well potential. We establish the existence of minimal heteroclinic solutions connecting the two wells of the…

We investigate the vacuum properties of a massless scalar field theory in constrained spatial geometry, namely, the instantaneous appearance of a thick Dirichlet boundary inside a one-dimensional (1D) Dirichlet cavity and divides it into…

We initiate the study of weighted multi-Toeplitz operators associated with noncommutative regular domains in B(H)^n. These operators are acting on the full Fock space with n generators and have as symbols free pluriharmonic functions.…

Kahler manifolds have a natural hyperkahler structure associated with (part of) their cotangent bundles. Using projective superspace, we construct four-dimensional N = 2 models on the tangent bundles of some classical Hermitian symmetric…

This is the first paper in a series of investigation of the pluripotential theory on Teichm\"uller space. The main purpose of this paper is to give an alternative approach to the Krushkal formula of the pluricomplex Green function on…

In this paper we solve the Dirichlet problems for different classes of plurisubharmonic functions on compact sets in $\mathbb C^n$ including continuous, pluriharmonic and maximal functions.

We introduce a large family of reproducing kernel Hilbert spaces $\mathcal{H} \subset \mbox{Hol}(\mathbb{D})$, which include the classical Dirichlet-type spaces $\mathcal{D}_\alpha$, by requiring normalized monomials to form a Riesz basis…

We introduce a new functional space U designed to contain all classical arithmetic functions (Mobius, von Mangoldt, Euler phi, divisor functions, Dirichlet characters, etc.). The norm of U combines a Hilbert-type component, based on square…

For any compact set $K\subset \mathbb{R}^n$ we develop the theory of Jensen measures and subharmonic peak points, which form the set $\mathcal{O}_K$, to study the Dirichlet problem on $K$. Initially we consider the space $h(K)$ of functions…

Suppose $(X,\omega)$ is a compact K\"ahler manifold of dimension $n$, and $\theta$ is closed $(1,1)$-form representing a big cohomology class. We introduce a metric $d_1$ on the finite energy space $\mathcal{E}^1(X,\theta)$, making it a…

The Dirichlet problem for a Monge-Ampere equation corresponding to a nonnegative, possible degenerate cohomology class on a Kaehler manifold with boundary is studied. C^{1,\alpha} estimates away from a divisor are obtained, by combining…

Given a compact polarized K\"ahler manifold $X\hookrightarrow\mathbb{CP}^N$, the space of Bergman metrics on $X$, parameterized by $\mathrm{SL}(N+1,\mathbb{C})$, corresponds to a dense set in the space of K\"ahler potentials in the K\"ahler…

We give a version of the Montel theorem for Hardy spaces of holomorphic functions on an infinite dimensional space. As a by-product, we provide a Montel-type theorem for the Hardy space of Dirichlet series. This approach also gives an…

In this paper, we introduce a general class of weighted spaces of holomorphic Dirichlet series (with real frequencies) analytic in some half-plane and study composition operators on these spaces. In the particular case when the symbol…

Under the action of the c-map, special Kahler manifolds are mapped into a class of quaternion-Kahler spaces. We explicitly construct the corresponding Swann bundle or hyperkahler cone, and determine the hyperkahler potential in terms of the…

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…

Given $1<p<N$ and two measurable functions $V(r)\geq 0$ and $K(r)>0$, $r>0$, we define the weighted spaces \[ W=\left\{ u\in D^{1,p}(\mathbb{R}^N):\int_{\mathbb{R}^N}V\left(\left|x\right|\right) \left|u\right|^p dx<\infty \right\} , \quad…

Combining probabilistic and analytic tools from potential theory, we investigate Dirichlet problems associated with the Dunkl Laplacian $\Delta_k$. We establish, under some conditions on the open set $D\subset\R^d$, the existence of a…

This is (raw) lecture notes of the course read on 6th European intensive course on Complex Analysis (Coimbra, Portugal) in 2000. Our purpose is to describe a general framework for generalizations of the complex analysis. As a consequence a…

We introduce the basic concepts related to subharmonic functions and potentials, mainly for the case of the complex plane and prove the Riesz decomposition theorem. Beyond the elementary facts of the theory we deviate slightly from the…