Related papers: On the Shilov boundary ideal for Fr\'{e}chet local…

We recently introduced a scale of kernel-based greedy schemes for approximating the solutions of elliptic boundary value problems. The procedure is based on a generalized interpolation framework in reproducing kernel Hilbert spaces and was…

We are interested in numerical algorithms for computing the electrical field generated by a charge distribution localized on scale $l$ in an infinite heterogeneous correlated random medium, in a situation where the medium is only known in a…

We study Dirichlet forms defined by nonintegrable L\'evy kernels whose singularity at the origin can be weaker than that of any fractional Laplacian. We show some properties of the associated Sobolev type spaces in a bounded domain, such as…

We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…

In Part I we construct the upper bound, in the spirit of $\Gamma$- $\limsup$, achieved by multidimensional profiles, for some general classes of singular perturbation problems, with or without the prescribed differential constraint, taking…

This paper develops a new Hilbert space method to characterize a family of reproducing kernel Hilbert spaces of real harmonic functions in a bounded Lipschitz domain $\Omega \subset \mathbb R^d, d\geq 2$ involving some families of positive…

In this paper a quantum analog of the $*$-algebra of regular functions on the Shilov boundary $S(\mathbb D)$ of bounded symmetric domain $\mathbb D$ is constructed. The algebras of regular functions on $S(\mathbb D)$ are described in terms…

Let $G$ be a semiabelian variety defined over an algebraically closed field $K$, endowed with a rational self-map $\Phi$. Let $\alpha\in G(K)$ and let $\Gamma\subseteq G(K)$ be a finitely generated subgroup. We show that the set…

This work produces a q-analogue of the Cauchi-Szeg\"o integral representation that retrieves a holomorphic function in the matrix ball from its values on the Shilov boundary. Besides that, the Shilov boundary of the quantum matrix ball is…

We show that independent and uniformly distributed sampling points are as good as optimal sampling points for the approximation of functions from the Sobolev space $W_p^s(\Omega)$ on bounded convex domains $\Omega\subset \mathbb{R}^d$ in…

We generalize Fulton's Residual Intersection Theorem for the Segre class and express the Segre classes of schemes with regularly embedded components in terms of the Chern classes of the normal bundles to the components and their…

In this paper, we investigate the existence of weak solution for a Kirchhoff type problem driven by a nonlocal operator of elliptic type in a fractional Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions {\small$$…

The Boutet de Monvel calculus of pseudo-differential boundary operators is generalised to the full scales of Besov and Triebel--Lizorkin spaces (though with finite integral exponents for the latter). The continuity and Fredholm properties…

In our companion paper (S.N. Chandler Wilde, D.P. Hewett, A. Moiola, Sobolev spaces on non-Lipschitz subsets of $\mathbb{R}^n$ with application to boundary integral equations on fractal screens, 2016) we studied a number of different…

We study perfect matchings on the rail-yard graphs in which the right boundary condition is given by the empty partition and the left boundary can be divided into finitely many alternating line segments where all the vertices along each…

Some skew-symmetrizable integer exchange matrices are associated to ideal (tagged) triangulations of marked bordered surfaces. These exchange matrices admits unfoldings to skew-symmetric matrices. We develop an combinatorial algorithm that…

We study the optimization of Steklov eigenvalues with respect to a boundary density function $\rho$ on a bounded Lipschitz domain $\Omega \subset \mathbb{R}^N$. We investigate the minimization and maximization of $\lambda_k(\rho)$, the…

Asymptotic formulae for Green's kernels $G_\epsilon({\bf x}, {\bf y})$ of various boundary value problems for the Laplace operator are obtained in regularly perturbed domains and certain domains with small singular perturbations of the…

We consider a family of open sets $M_\epsilon$ which shrinks with respect to an appropriate parameter $\epsilon$ to a graph. Under the additional assumption that the vertex neighbourhoods are small we show that the appropriately shifted…

We consider fractional Sobolev spaces $H^\theta(\Gamma)$, $\theta \in [0,1]$, on a 2D surface $\Gamma$. We show that functions in $H^\theta(\Gamma)$ can be decomposed into contributions with local support in a stable way. Stability of the…