Related papers: Approximation of plurisubharmonic functions on com…
In this paper, we introduce a new subclass of close-to-convex harmonic functions. We present a sufficient coefficient condition for a function to be a member of this class. Furthermore, we establish a distortion theorem. These results lay…
We give a sufficient condition on a sequence of uniformly bounded $\omega$-plurisubharmonic functions, $\omega$ being a Hermitian metric, for which the sequence of associated Monge-Amp\`ere measures converges weakly. This criterion can be…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
We show that on separable Banach spaces admitting a separating polynomial, any uniformly continuous, bounded, real-valued function can be uniformly approximated by Lipschitz, analytic maps on bounded sets.
We investigate the question of existence of plurisubharmonic defining functions for smoothly bounded, pseudoconvex domains in $\mathbb{C}^2$. In particular, we construct a family of simple counterexamples to the existence of…
Given sufficiently many components, it is often cited that finite mixture models can approximate any other probability density function (pdf) to an arbitrary degree of accuracy. Unfortunately, the nature of this approximation result is…
We establish plurisubharmonicity of the envelope of Poisson and Lelong functionals on almost complex manifolds. That is, we generalize the corresponding results for complex manifolds and almost complex manifolds of complex dimension two. We…
Let T be a positive plurisubharmonic current of bidimension (p,p) and let $\delta>0$. Assume that the Lelong number of T satisfies $\nu(T,a)\geq \delta$ on a dense subset of supp(T) (rectifiable currents satisfy this condition). Then…
We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…
Pseudo-holomorphic curves on almost complex manifolds have been much more intensely studied than their "dual" objects, the plurisubharmonic functions. These functions are defined classically by requiring that the restriction to each…
The main purpose of this paper is to introduce and study the notion of plurifinely-maximal plurifinely plurisubharmonic functions, which extends the notion of maximal plurisubharmonic functions on a Euclidean domain to a plurifine domain of…
In this paper, we combine tools from pluripotential theory and commutative algebra to study singularity invariants of plurisubharmonic functions. We establish several relationships between the singularity invariants of plurisubharmonic…
In this course of lectures we give an account of the growth theory of subharmonic functions, which is directed towards its applications to entire functions of one and several complex variables.
This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…
The goal of this article is to present a survey of the recent theory of plurisubharmonic functions of quaternionic variables, and its applications to theory of valuations on convex sets and HKT-geometry (HyperK\"ahler with Torsion). The…
In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.
We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…
We give direct and inverse theorems for the weighted approximation of functions with endpoint singularities by combinations of Bernstein operators.
Let $D$ be a bounded domain in $\mathbb C^n$. We study approximation of (not necessarily bounded from above) $m-$subharmonic function $D$ by continuous $m-$subharmonic ones defined on neighborhoods of $\overline{D}$. We also consider the…
The purpose of this paper is to provide some properties of maximal plurisubharmonic functions in a bounded domain of \mathbb{C}^n