Related papers: Non-polynomial divided difference and blossoming
Polynomials which afford nonnegative, real-rooted symmetric decompositions have been investigated recently in algebraic, enumerative and geometric combinatorics. Br\"and\'en and Solus have given sufficient conditions under which the image…
We give a new combinatorial interpretation of the stationary distribution of the (partially) asymmetric exclusion process on a finite number of sites in terms of decorated alternative trees and colored permutations. The corresponding…
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…
This paper investigates two important analytical properties of hyperbolic-polynomial penalized splines, HP-splines for short. HP-splines, obtained by combining a special type of difference penalty with hyperbolic-polynomial B-splines…
The richly developed theory of complex manifolds plays important roles in our understanding of holomorphic functions in several complex variables. It is natural to consider manifolds that will play similar roles in the theory of holomorphic…
Finite dimensional subspaces spanned by exponential functions in the space of square integrable functions on a finite interval of the real line are considered. Their limiting positions are studied and described in terms of expo-polynomials.
In this article, families of non-linear subdivision schemes are presented that are based on univariate polynomials up to degree three. Theses families of schemes are constructed by using dynamic iterative re-weighed least squares method.…
We give a new proof that bounded non-commutative functions on polynomial polyhedra can be represented by a realization formula, a generalization of the transfer function realization formula for bounded analytic functions on the unit disk.
This paper mainly studies the quadratic growth and the strong metric subregularity of the subdifferential of a function that can be represented as the sum of a function twice differentiable in the extended sense and a subdifferentially…
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…
Polynomial and spline quasi-interpolants (QIs) are practical and effective approximation operators. Among their remarkable properties, let us cite for example: good shape properties, easy computation and evaluation (no linear system to…
For one-matrix models with polynomial potentials, the explicit relationship between the partition function and the isomonodromic tau function for the 2x2 polynomial differential systems satisfied by the associated orthogonal polynomials is…
We prove a structural result for degree-$d$ polynomials. In particular, we show that any degree-$d$ polynomial, $p$ can be approximated by another polynomial, $p_0$, which can be decomposed as some function of polynomials $q_1,...,q_m$ with…
We introduce the notion of non commutative truncated polynomial extension of an algebra A. We study two families of these extensions. For the first one we obtain a complete classification and for the second one, which we call upper…
We construct a set $M_d$ whose points parametrize families of Meixner polynomials in $d$ variables. There is a natural bispectral involution $b$ on $M_d$ which corresponds to a symmetry between the variables and the degree indices of the…
We investigate properties of differential and difference operators annihilating certain finite-dimensional subspaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and…
Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of random orthonormal polynomials with increasing dimensions. This…
Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the…
Sitting at the top level of the Askey-scheme, Wilson polynomials are regarded as the most general hypergeometric orthogonal polynomials. Instead of a differential equation, they satisfy a second order Sturm-Liouville type difference…
multiplication operator on a Hilbert space may be approximated with finite sections by choosing an orthonormal basis of the Hilbert space. Nonzero multiplication operators on $L^2$ spaces of functions are never compact and then such…