In this paper, we introduce a general class of weighted spaces holomorphic Dirichlet series (with real frequencies) analytic in some half-plane and study composition operators on these spaces. the particular case when symbol inducing operator is an affine function, give criteria for boundedness compactness. We also cyclicity property as byproduct characterization so that direct sum identity plu...

We study the boundary theory of a connected weighted graph G from the viewpoint of stochastic integration. For the Hilbert space HE of Dirichlet-finite functions on G, we construct a Gel’fand triple S ⊆ HE ⊆ S′. This yields a probability measure P on S′ and an isometric embedding of HE into L2(S′,P), and hence gives a concrete representation of the boundary as a certain class of “distributions”...

We consider the space-time boundary element method (BEM) for heat equation with prescribed initial and Dirichlet data. propose a residual-type posteriori error estimator that is lower bound and, up to weighted $L_2$-norms of residual, also an upper unknown BEM error. The possibly locally refined meshes are assumed be prismatic, i.e., their elements tensor-products $J\times K$ in time $J$ space ...

We compute Poisson kernels for integer weight parameter standard weighted biharmonic operators in the unit disc with Dirichlet boundary conditions. The computations performed extend the supply of explicit examples of such kernels and suggest similar formulas for these Poisson kernels to hold true in more generality. Computations have been carried out using the open source computer algebra packa...

In this work we characterize boundedness and compactness of weighted composition operators acting between Dirichlet type spaces by using Carleson measures. We also find essential norm estimates for these operators.

In this paper we prove some a priori bounds for the solutions of the Dirichlet problem for elliptic equations with singular coefficients in weighted Sobolev spaces. Mathematics subject classification (2010): 35J25, 35B45, 35R05.

We prove a well-posedness result for second order boundary value problems in weighted Sobolev spaces on curvilinear polyhedral domains in Rn with Dirichlet boundary conditions. Our typical weight is the distance to the set of singular boundary points.