Related papers: Special polyhedra for Reinhardt domains

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…

Let $1\leq m\leq n$ be two fixed integers. Let $\Omega \Subset \mathbb C^n$ be a bounded $m$-hyperconvex domain and $\mathcal A \subset \Omega \times ]0,+ \infty[$ a finite set of weighted poles. We define and study properties of the…

A characterization of non-hyperbolic pseudoconvex Reinhardt domains in $\mathbb C^2$ for which the answer to the Serre problem is positive is given.

We complete the complexity classification by degree of minimizing a polynomial over the integer points in a polyhedron in $\mathbb{R}^2$. Previous work shows that optimizing a quadratic polynomial over the integer points in a polyhedral…

In the space of holomorphic functions in a convex domain it is studied the interpolation problem by means of sums of the series of exponentials converging uniformly on all compact sets of the domain. The discrete set of the interpolation…

Let $K$ be a compact convex body in $\mathbb R^n.$ For any affine line $L,$ denote $\widehat{\chi}_K(L)=\int_{L}\chi_K(x)dl(x),$ where $dl$ is the arc length measure, the $X$-ray transform of the characteristic function $\chi_K,$ i.e., the…

We provide a new representation of a refinable shift invariant space with a compactly supported generator, in terms of functions with a special property of homogeneity. In particular these functions include all the homogeneous polynomials…

In this paper, we prove a generalization of Green's Hyperplane Restriction Theorem to the case of modules over the polynomial ring, providing in particular an upper bound for the Hilbert function of the general linear restriction of a…

In this paper we consider basic hypergeometric functions introduced by Heine. We study mapping properties of certain ratios of basic hypergeometric functions having shifted parameters and show that they map the domains of analyticity onto…

The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…

Let $D\subset \mathbb{R}^d$ be a bounded Lipschitz domain, $\omega$ be a high order modulus of continuity and let $T$ be a convolution Calder\'{o}n-Zygmund operator. We characterize the bounded restricted operators $T_D$ on the Zygmund…

We prove in an elementary way that for a Lipschitz domain $D\subset \cn$, all plurisubharmonic functions on $D$ can be regularized near any boundary point.

We investigate problems related with the existence of square integrable holomorphic functions on (unbounded) balanced domains. In particular, we solve the problem of Wiegerinck for balanced domains in dimension two. We also give a…

We use the method of pseudoanalytic continuation to obtain a characterization of spaces of holomorphic functions with boundary values in Besov spaces in terms of polynomial approximations.

In this paper, we show that the convex domains of the hyperbolic space which are almost extremal for the Faber-Krahn or the Payne-Polya-Weinberger inequalities are close to geodesic balls. Our proof is also valid in other space forms and…

This paper considers the approximation of spatial convolution with a given radial integral kernel. Previous studies have demonstrated that approximating spatial convolution using a system of partial differential equations (PDEs) can…

We introduce a method to estimate the size of the domain of definition of the solutions of a meromorphic vector field on a neighborhood of its pole divisor. The corresponding techniques are, in a certain sense, quantitative versions of some…

We give sufficient conditions on planar domains for polynomials to be dense in the algebras A and A-infinity of the product of these domains, endowed with their natural topologies. We also characterize the uniform limits, with respect to…

In this paper we give some results about the approximation of a Lipschitz function on a Banach space by means of $\Delta$-convex functions. In particular, we prove that the density of $\Delta$-convex functions in the set of Lipschitz…

We explicitly compute the Dolbeault cohomologies of certain domains in complex space generalizing the classical Hartogs figure. The cohomology groups are non-Hausdorff topological vector spaces, and it is possible to identify the reduced…