Related papers: Discrete Polynomials and Discrete Holomorphic Appr…
Using purely combinatorial means we obtain results on simultaneous Diophantine approximation modulo 1 for systems of polynomials with real coefficients and no constant term.
Some Dirichlet-like functions, attached to a pair (periodic function, polynomial) are introduced and studied. These functions generalize the standard Dirichlet L-functions of Dirichlet characters. They have similar properties, being…
Using results from theory of operators on a Hilbert space, we prove approximation results for matrix-valued holomorphic functions on the unit disc and the unit bidisc. The essential tools are the theory of unitary dilation of a contraction…
By the celebrated Weierstrass Theorem the set of algebraic polynomials is dense in the space of continuous functions on a compact set in R^d. In this paper we study the following question: does the density hold if we approximate only by…
We study best approximation to a given function, in the least square sense on a subset of the unit circle, by polynomials of given degree which are pointwise bounded on the complementary subset. We show that the solution to this problem, as…
We introduce holomorphic Riemannian maps between almost Hermitian manifolds as a generalization of holomorphic submanifolds and holomorphic submersions, give examples and obtain a geometric characterization of harmonic holomorphic…
We continue our investigation of Discrete Riemann Surfaces with the discussion of the discrete analogs of period matrices, Riemann's bilinear relations, exponential of constant argument, series and electrical moves. We show that given a…
The purpose of this paper is to study holomorphic approximation and approximation of $\bar\partial$-closed forms in complex manifolds of complex dimension $n\geq 1$. We consider extensions of the classical Runge theorem and the Mergelyan…
We prove that the Newton product of efficient polynomial projectors is still efficient. Various polynomial approximation theorems are established involving Newton product projectors on spaces of holomorphic functions on a neighborhood of a…
In this paper, approximation by means of algebraic polynomials of classes of functions defined by a generalised modulus of smoothness of operators of differentiation of these functions is considered. We give structural characteristics of…
Final representation of all those measures $\mu$ for which algebraic polynomials are dense in $L_p(R, d\mu)$ is found. The weighted analogue of the Weierstrass polynomial approximation theorem and a new version of the M. Krein's theorem…
We consider an equation of multiple variables in which a partial derivative does not vanish at a point. The implicit function theorem provides a local existence and uniqueness of the function for the equation. In this paper, we propose an…
We provide some conditions for the graph of a Hoelder-continuous function on \bar{D}, where \bar{D} is a closed disc in the complex plane, to be polynomially convex. Almost all sufficient conditions known to date --- provided the function…
We describe and study geometric properties of discrete circular and spherical means of directional derivatives of functions, as well as discrete approximations of higher order differential operators. For an arbitrary dimension we present a…
Generalizations of some known results on the best, best linear and best one-sided approxima- tions by trigonometric polynomials of the classes of 2\pi - periodic functions presented in the form of convolutions to the case of set-valued…
Let D be a domain in C^n with smooth boundary, of finite 1-type at a point p in the boundary and such that the closure of D has a basis of Stein Runge neighborhoods. Assume that there exists an analytic disc which intersects the closure of…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
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…
We extend a classical approximation result of harmonic functions in planar domains due to Bernstein and Walsch to the setting of harmonic functions in Riemann surfaces. This result gives an exact characterization of the rate at which a…
There is presented an approach to find an approximation polynomial of a function with two variables based on the two dimensional discrete Fourier transform. The approximation polynomial is expressed through Chebyshev polynomials. There is…