Related papers: Approximation by polynomials on quaternionic compa…
The different notions of matings of pairs of equal degree polynomials are introduced and are related to each other as well as known results on matings. The possible obstructions to matings are identified and related. Moreover the relations…
We revisit the approximation of nonempty compact planar sets by filled-in Julia sets of polynomials developed by Lindsey and Younsi and analyze the rate of approximation. We use slightly modified fundamental Lagrange interpolation…
We obtain new partial results supporting the spectral set conjecture in dimension 1.
We propose and investigate two new methods to approximate $f({\bf A}){\bf b}$ for large, sparse, Hermitian matrices ${\bf A}$. The main idea behind both methods is to first estimate the spectral density of ${\bf A}$, and then find…
We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using…
The notion of $p$-compact sets arises naturally from Grothendieck's characterization of compact sets as those contained in the convex hull of a norm null sequence. The definition, due to Sinha and Karn (2002), leads to the concepts of…
This paper is a continuation of the research of our previous work and considers quaternionic generalized Carath\'eodory functions and the related family of generalized positive functions. It is addressed to a wide audience which includes…
We consider the approximation properties of finite element spaces on quadrilateral meshes. The finite element spaces are constructed starting with a given finite dimensional space of functions on a square reference element, which is then…
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…
In this article, a novel method to compute all discrete polyharmonic functions in the quarter plane for models with small steps, zero drift and a finite group is proposed. A similar method is then introduced for continuous polyharmonic…
Let F be a holomorphic map whose components satisfy some polynomial relations. We present an algorithm for constructing Nash maps locally approximating F, whose components satisfy the same relations.
The density of polynomials in a weighted space of infinitely differentiable functions in a multidimensional real space is proved under minimal conditions on weight functions and on differences between weight functions. We apply this result…
In this paper we solve the Dirichlet problems for different classes of plurisubharmonic functions on compact sets in $\mathbb C^n$ including continuous, pluriharmonic and maximal functions.
The suitable basis functions for approximating periodic function are periodic, trigonometric functions. When the function is not periodic, a viable alternative is to consider polynomials as basis functions. In this paper we will point out…
We consider approximations of a continuous function on a countable normed Fr\'{e}chet space by analytic and $*$-analytic. Also we found a criterium of the existence of an extension of a continuous function from a dense subspace of a…
In this article, we show some density properties of smooth and compactly supported functions in fractional Musielak-Sobolev spaces essentially extending the results of Fiscella, Servadei, and Valdinoci obtained in the fractional Sobolev…
A method for computing integrals of polynomial functions on compact symmetric spaces is given. Those integrals are expressed as sums of functions on symmetric groups.
Recently, Charpentier showed that there exist holomorphic functions $f$ in the unit disk such that, for any proper compact subset $K$ of the unit circle, any continuous function $\phi$ on $K$ and any compact subset $L$ of the unit disk,…
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.
We take a unifying and new approach toward polynomial and trigonometric approximation in an arbitrary number of variables, resulting in a precise and general ready-to-use tool that anyone can easily apply in new situations of interest. The…