Related papers: Sampling and interpolation for analytic selfmappin…
Based on the recently proved Khavinson conjecture, we establish an inequality of Schwarz-Pick type for harmonic functions on the unit ball of $\mathbb{R}^n$.
In this paper we discuss the problem of interpolation on straight lines by linear combinations of ridge functions with fixed directions. By using some geometry and/or systems of linear equations, we constructively prove that it is…
We consider the problem of discretizing one-dimensional, real-valued functions as graphs. The goal is to find a small set of points, from which we can approximate the remaining function values. The method for approximating the unknown…
Given a sequence of real numbers, we consider its subsequences converging to possibly different limits and associate to each of them an index of convergence which depends on the density of the associated subsequences. This index turns out…
This paper reports on constructive approximation methods for three classes of holomorphic functions on the unit disk which are closely connected each other: the class of starlike and spirallike functions, the class of semigroup generators,…
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 consider large random graphs with prescribed degrees, such as those generated by the configuration model. In the regime where the empirical degree distribution approaches a limit $\mu$ with finite mean, we establish the systematic…
We consider non-linear generalizations of fractal interpolating functions applied to functions of one and two variables. The use of such interpolating functions in resizing images is illustrated.
Graph signal sampling is the problem of selecting a subset of representative graph vertices whose values can be used to interpolate missing values on the remaining graph vertices. Optimizing the choice of sampling set using concepts from…
In 2002 C. Berg, Y. Chen, and M. Ismail found a nice relation between the determinancy of the Hamburger moment problem and asymptotic behavior of the smallest eigenvalues of the corresponding Hankel matrices. We investigate whether an…
The problem of interpolation at $(n+1)^2$ points on the unit sphere $\mathbb{S}^2$ by spherical polynomials of degree at most $n$ is proved to have a unique solution for several sets of points. The points are located on a number of circles…
One of the possible variants of the classification of trigonometric interpolation splines is considered, depending on the chosen convergence factors, the distribution of signs of the basis functions and the interpolation factors. The…
We present several results associated to a holomorphic-interpolation problem for the spectral unit ball \Omega_n, n\geq 2. We begin by showing that a known necessary condition for the existence of a $\mathcal{O}(D;\Omega_n)$-interpolant (D…
Interpolation Theory gives techniques for constructing spaces from two initial Banach spaces. We provide several conditions under which the restriction of a holomorphic map $f:X_0+X_1 \rightarrow Y_0+Y_1$ to the interpolated spaces (using…
In \cite{ds_hfs}, a geometric procedure for constructing a Nevanlinna-Pick problem on $\D^n$ with a specified set of uniqueness was established. In this sequel we conjecture a necessary and a sufficient condition for a Nevanlinna-Pick…
We construct polynomial approximations of Dzjadyk type (in terms of the k-th modulus of continuity, $k \ge 1$) for analytic functions defined on a continuum E in the complex plane, which simultaneously interpolate at given points of E.…
We consider interpolation inequalities for imbeddings of the $l^2$-sequence spaces over $d$-dimensional lattices into the $l^\infty_0$ spaces written as interpolation inequality between the $l^2$-norm of a sequence and its difference. A…
Interpolation is an important property of classical and many non classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the propositional version of the…
The synthesis of optimization algorithms typically follows a design-first-analyze-later approach, which often obscures fundamental performance limitations and hinders the systematic design of algorithms operating at the achievable…
We introduce a novel collection of uniqueness problems, with related sampling and interpolation issues. We call them deep zero problems, as they are concerned with local properties at a small number of given points.