Related papers: Multivariate orthogonal spline systems
We obtain exact, simple and very compact expressions for the linearization coefficients of the products of orthogonal polynomials; both the conventional Clebsch-Gordan-type and the modified version. The expressions are general depending…
In this note, we give sufficient conditions for the almost sure and the convergence in $\mathbb{L}^p$ of a $U$-statistic of order $m$ built on a strictly stationary but not necessarily ergodic sequence.
In this paper, we obtain infinitely many solutions for a class of quasilinear Schr\"{o}dinger-Poisson system which is coupled by a Schr\"{o}dinger equation of $p$-Laplacian and a Poisson equation of $q$-Laplacian, involving with concave and…
For a connected semisimple algebraic group $G$, we consider some special infinite series of tensor products of simple $G$-modules whose $G$-fixed point spaces are at most one-dimensional. We prove that their existence is closely related to…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
We construct smooth localized orthonormal bases compatible with homogeneous mixed-norm Triebel-Lizorkin spaces in an anisotropic setting on $\bR^d$. The construction is based on tensor products of so-called univariate brushlet functions…
We prove some sufficient conditions implying $l^p$ inequalities of the form $||x||_p \leq ||y||_p$ for vectors $ x, y \in [0,\infty)^n$ and for $p$ in certain positive real intervals. Our sufficient conditions are strictly weaker than the…
We prove regularity estimates for time derivatives of a large class of nonlinear parabolic partial differential systems. This includes the instationary (symmetric) p-Laplace system and models for non Newtonien fluids of powerlaw or Carreau…
A class of trigonometric interpolation splines depending on parameter vectors, selected convergence factors and interpolation factors is considered. The concept of crosslink grids and interpolation grids is introduced; these grids can match…
We study orthogonal polynomial systems arising from general pre-Hilbert inner products on polynomial spaces, beyond the classical framework of measures. To each such inner product we associate a canonical Laplacian defined from an abstract…
The aim of this article is to show the existence, and also give an explicit construction, of infinite sets of orthogonal exponentials for certain families of convex polytopes which include simple-rational polytopes and also non simple…
We study two families of orthogonal polynomials. The first is a finite family related to the Askey-Wilson polynomials but the orthogonality is on the real line. A limiting case of this family is an infinite system of orthogonal polynomials…
Higher order tensor inversion is possible for even order. We have shown that a tensor group endowed with the Einstein (contracted) product is isomorphic to the general linear group of degree $n$. With the isomorphic group structures, we…
We consider a class of nonautonomous parabolic first-order coupled systems in the Lebesgue space $L^p({\mathbb R}^d;{\mathbb R}^m)$, $(d,m \ge 1)$ with $p\in [1,+\infty)$. Sufficient conditions for the associated evolution operator ${\bf…
In this paper, we consider some aspects of the physics of the partly pinned (PP) systems obtained by freezing in place particles in equilibrium bulk fluid configurations in the normal (nonglassy) state. We first discuss the configurational…
We investigate the relation between multilinear mappings and multipartite states. We show that the isomorphism between multilinear mapping and tensor product completely characterizes decomposable multipartite states in a mathematically…
It is be shown that the sequence of Bernstein polynomials for a function of several variables converges to this function uniformly along with every partial derivative of any order, provided that the latter derivative is well defined and…
In this paper we have discussed different possible orthogonalities in matrices, namely orthogonal, quasi-orthogonal, semi-orthogonal and non-orthogonal matrices including completely positive matrices, while giving some of their…
We consider symmetric partial exclusion and inclusion processes in a general graph in contact with reservoirs, where we allow both for edge disorder and well-chosen site disorder. We extend the classical dualities to this context and then…
This note attempts to study lacunary trigonometric products with values in the matrix group SU(1,1) in analogy with lacunary trigonometric series. The central questions are the characterization of their convergence in an appropriately…