Related papers: Boundary representation of Dirichlet forms on disc…
We study indecomposable representations of quivers on separable infinite-dimensional Hilbert spaces by bounded operators. We consider a complement of Gabriel's theorem for these representations. Let $\Gamma$ be a finite, connected quiver.…
Bounds on the minimum degree and on the number of vertices at- taining it have been much studied for finite edge-/vertex-minimally k- connected/k-edge-connected graphs. We give an overview of the results known for finite graphs, and show…
We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known…
We introduce a broad class of equations that are described by a graph, which includes many well-studied systems. For these, we show that the number of solutions (or the dimension of the solution set) can be bounded by studying certain…
We describe constructions of infinite graphs which are not representable as integral graphs in the plane, addressing a question of Erd\H{o}s. We also mention some related problems.
In this paper, we develop the infinitesimal geometry of the limit spaces of compact Riemannian manifolds with boundary, where we assume lower bounds on the sectional curvatures of manifolds and boundaries and the second fundamental forms of…
In this note we present some abstract ideas how one can construct spaces from building blocks according to a graph. The coupling is expressed via boundary pairs, and can be applied to very different spaces such as discrete graphs, quantum…
We study asymptotic behaviors of solutions $f$ to the Dirichlet problem for minimal graphs in the hyperbolic space with singular asymptotic boundaries under the assumption that the boundaries are piecewise regular with positive curvatures.…
Continuous limits of discrete systems with long-range interactions are considered. The map of discrete models into continuous medium models is defined. A wide class of long-range interactions that give the fractional equations in the…
We study the Dirichlet problem at infinity on a Cartan-Hadamard manifold for a large class of operators containing in particular the p-Laplacian and the minimal graph operator.
We prove upper bounds on the face numbers of simplicial complexes in terms on their girths, in analogy with the Moore bound from graph theory. Our definition of girth generalizes the usual definition for graphs.
We provide decompositions of Dirichlet forms into recurrent and transient parts as well as into conservative and dissipative parts, in the framework of Hausdorff state spaces. Combining both formulae we write every Dirichlet form as the sum…
We extend the method of layer potentials to manifolds with boundary and cylindrical ends. To obtain this extension along the classical lines, we have to deal with several technical difficulties due to the non-compactness of the boundary,…
We study a Dirichlet problem for the heat equation in a domain containing an interior hole. The domain has a fixed outer boundary and a variable inner boundary determined by a diffeomorphism $\phi$. We analyze the maps that assign to the…
A complete classification and character formulas for finite-dimensional irreducible representations of the rational Cherednik algebra of type A is given. Less complete results for other types are obtained. Links to the geometry of affine…
After a quick review of the representation theory of the symmetric group, we give an exposition of the tools brought about by the so-called half-infinite wedge representation of the infinite symmetric group. We show how these can be applied…
We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space.…
In this paper, we consider a biharmonic equation with respect to the Dirichlet problem on a domain of a locally finite graph. Using the variation method, we prove that the equation has two distinct solutions under certain conditions.
We introduce torsoids, a canonical structure in matching covered graphs, corresponding to the bricks and braces of the graph. This allows a more fine-grained understanding of the structure of finite and infinite directed graphs with respect…
We consider the inhomogeneous Dirichlet problem on product domains. The main result is the asymptotic expansion of the solution in terms of increasing smoothness up to the boundary. In particular, we show the exact nature of the…