Related papers: Bivariate Lagrange interpolation at the Padua poin…
In this paper we study the consequences of overinterpolation, i.e., the situation when a function can be interpolated by polynomial, or rational, or algebraic functions in more points that normally expected. We show that in many cases such…
The Casas-Alvero conjecture is about interpolation polynomials. There are some partial proofs of it, but there is not any proof in the general case.In this paper we propose three.
We prove that for almost square tensor product grids and certain sets of bivariate polynomials the Vandermonde determinant can be factored into a product of univariate Vandermonde determinants. This result generalizes the conjecture [Lemma…
The present paper studies the existence of valuative interpolation on the local ring of an irreducible analytic subvariety at singular points. We firstly develop the concepts and methods of Zhou weights and Tian functions near singular…
A $\textit{polygonal curve}$ is a collection of $m$ connected line segments specified as the linear interpolation of a list of points $\{p_0, p_1, \ldots, p_m\}$. These curves may be obtained by sampling points from an oriented curve in…
We propose a class of Pad\'e interpolation problems whose solutions are expressible in terms of determinants of hypergeometric series.
Uniform interpolation properties are defined for equational consequence in a variety of algebras and related to properties of compact congruences on first the free and then the finitely presented algebras of the variety. It is also shown,…
Laplace interpolation is a popular approach in image inpainting using partial differential equations. The classic approach considers the Laplace equation with mixed boundary conditions. Recently a more general formulation has been proposed…
It is shown that, given any finite dimensional, split basic algebra $\Lambda = K\Gamma/I$ (where $\Gamma$ is a quiver and $I$ an admissible ideal in the path algebra $K \Gamma$), there is a finite list of affine algebraic varieties, the…
We study positive solutions of the equation $-\Delta_g u + \lambda u = \lambda u^q$, with $\lambda >0$, $q>1$ on the round sphere $\mathbb{S}^n$ . We reduce the equation to an ordinary differential equation by considering isoparametric…
A constructive procedure is given to determine all ideals of a solvable Lie algebra. This is used in determining algorithmically all conjugacy classes of subalgebras of a given solvable Lie algebra.
We discuss a question which relates to Calderon's complex interpolation method. More precisely, we will consider the so-called "periodic" complex interpolation method, studied by Peetre. (Which also corresponds to the spaces obtained by…
Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is a theorem of A. Pitts, which shows that uniform interpolation holds for intuitionistic…
Ordinary infinitary languages L_{lambda, kappa} satisfy the Interpolation Theorem only in the case lambda <= {aleph_1}, kappa = {aleph_0}, this include first order logic of course. There are also some pairs of such logics satifying…
In a previous paper, we derived necessary and sufficient conditions for the invertibility of square submatrices of the Pascal upper triangular matrix. To do so, we established a connection with the two-point Birkhoff interpolation problem.…
A class of generalized Wess-Zumino models with distinct vacua is investigated. These models allow for BPS saturated vacua interpolation along one compact spatial dimension. The properties of these interpolations are studied.
We study the interpolation group whose elements are suitable pairs of formal power series. This group has a faithful representation into infinite lower triangular matrices and carries thus a natural structure as a Lie group. The matrix…
This paper deals with variety of problems in pcf theory and infinitary combinatorics. We look at normal filters and prc, measures of the size of [lambda]^{<kappa}, pcf-inaccessibility, entangled orders (and narrow Boolean Algebras),…
We give a natural geometric condition that ensures that sequences of Chung-Yao interpolation polynomials (of fixed degree) of sufficiently differentiable functions converge to a Taylor polynomial.
We discuss a pointwise numerical differentiation formula on multivariate scattered data, based on the coefficients of local polynomial interpolation at Discrete Leja Points, written in Taylor's formula monomial basis. Error bounds for the…